LUOA ALGEBRA II MODULE 10

Identify the graph of the ellipse.

(-2,2), (-8,-5), (-2,-12), (-2,-5), (-4,-5)

Identify the vertex of the parabola. x+4= 1/6 (y-7)^2

(-4,7)

Solve the system of equations by elimination.16x2 + 4y2 = 144x2 + y2 = 36

(0, ±6)

Solve the system of equations by elimination.9x2 + y2 = 81x2 + y2 = 81

(0, ±9)

Give all solutions to the following non-linear system of equations. y = x 2 − 6x −7 and x − y = 17

(2, −15) and (5, −12)

Identify the focus of the parabola. x-8 = - 1/20 (y+2)^2

(3,-2)

Identify the graph of the ellipse.

(3,7), (-1,4), (3,4), (3,1), (7,4)

Identify the graph of the ellipse.

(4,7), (1,3), (4,3), (4,-1), (7,3)

Identify the equation for the circle with center (−4, 5) and a radius of 2.

(x + 4)2 + (y − 5)2 = 4

Identify the equation for the circle with center (3, −2) and a radius of 6.

(x − 3)2 + (y + 2)2 = 36

Identify the equation for the circle with center (3, 7) that contains the point (9, 11).

(x − 3)2 + (y − 7)2 = 52

Center (5,7) Radius of /5

(x − 5)2 + (y − 7)2 = 5

Identify the standard form of the equation by completing the square.3x2 − 2y2 − 12x − 16y + 4 = 0

(y+4)^2/ 12 - (x-2)^2/ 8 = 1

Solve the system of equations by elimination.3x2 + 5y2 = 239x2 − 2y2 = 1

(±1, ±2)

Solve the system of equations by graphing.2x2 + 6y2 = 1682x2 + y2 = 43

(±3, ±5)

Solve the system of equations by elimination.4x2 + y2 = 64x2 − y2 = 16

(±4, 0)

Solve the system of equations by graphing.5x2 + 10y2 = 120x2 + y2 = 20

(±4, ±2)

Solve the system of equations by graphing.3x2 − y2 = 129x2 + 2y2 = 216

(±4, ±6)

Solve the system of equations by elimination.2x2 + 8y2 = 50x2 − y2 = 25

(±5, ±0)

Solve the system of equations by graphing.160x2 − 25y2 = 4002x2 + 2y2 = 338

(±5, ±12)

Solve the system of equations by elimination.3x2 + 6y2 = 1322x2 − 3y2 = 60

(±6, ±2)

Solve the system of equations by graphing.x2 − y2 = 202x2 + 3y2 = 120

(±6, ±4)

Solve the system of equations by graphing.2x2 + 3y2 = 4053x2 − 2y2 = 81

(±9, ±9)

Give all solutions to the following non-linear system of equations. y = x 2 − 4x −7 and x + y = 3

(−2, 5) and (5, −2)

An ellipse has foci F1(−2, 4) and F2(0, 7), and the point (4, 4) is on the ellipse. Identify the constant sum for the ellipse.

11

Identify the constant difference for a hyperbola with foci (−7, 0) and (7, 0) and a point on the hyperbola (10, 0).

14

An ellipse has foci F1(9, 0) and F2(11, 6), and the point (1, 6) is on the ellipse. Identify the constant sum for the ellipse.

20

Identify the constant difference for a hyperbola with foci (−6, 0) and (6, 0) and a point on the hyperbola (4, 0).

4

Identify the constant difference for a hyperbola with foci (0, −5) and (0, 5) and a point on the hyperbola (0, 3).

6

Identify the constant difference for a hyperbola with foci (−3, 0) and (3, 0) and a point on the hyperbola (7, 0).

6

An ellipse has foci F1(−5, 5) aF2(0, 7) and the point (0, 5) is on the ellipse. Identify the constant sum for the ellipse.

7

Which points on the graph shown are within 6 units of the point (2, 4)?

A,B,C,I

Identify the conic section that the given equation represents. (x-5)^2/9 + (y+16)^2/9 = 1

Circle

Identify the standard form of the equation by completing the square. Then identify the conic and its correct graph.−9x2 + 16y2 + 126x − 160y − 185 = 0

Hyperbola ONE IS GOING UP THE OTHER IS GOING DOWN (A sideways not connected "x" i guess)

Identify the conic section that the given equation represents.2x2 − 5xy + 2y2 − 11x − 7y − 4 = 0

NOT CIRCLE

Identify the conic section that the given equation represents.8x2 + 10xy − 3y2 − 2x + 4y − 2 = 0

NOT CIRCLE

Identify the axis of symmetry for the parabola. y-6= - 2/3 (x+2)^2

NOT Y=-2

Which points on the graph shown are within 5 units of the point (4, −3)?

P,Q,R

Identify the standard form of the equation by completing the square. Then identify the conic.4x2 − 25y2 + 24x + 100y − 164 = 0

WRONG ANSWER: (x+3)^2 - (y+2)^2 Hyperbola

Identify the center and the radius of a circle that has a diameter with endpoints at (5, 8) and (7, 6).

center is (6, 7); radius is ≈ 1.414.

Identify the center and the radius of a circle that has a diameter with endpoints at (−5, 9) and (3, 5).

center is (−1, 7); radius is ≈ 4.472.

Identify the conic section that the given equation represents. (x+2)^2/16 + (y+3)^2/16 = 1

circle

Identify the conic section that the given equation represents.3x2 + 3y2 + 32x − 26y − 41 = 0

circle

Graph the equation x2 + y2 = 100 on a graphing calculator. Identify the conic section. Then identify the center and intercepts for circles and ellipses, or the vertices and direction that the graph opens for parabolas and hyperbolas.

circle center: (0, 0) intercepts: (±10, 0), (0, ±10)

Graph the equation x2 + y2 = 81 on a graphing calculator. Identify the conic section. Then identify the center and intercepts for circles and ellipses, or the vertices and direction that the graph opens for parabolas and hyperbolas.

circle center: (0, 0) intercepts: (±9, 0), (0, ±9)

Identify the conic section that the given equation represents.5(x − 3)2 = 20 − 4(y − 6)2

eclipse

Identify the conic section that the given equation represents.8x2 − 2xy + 4y2 + 20x − 5y − 12 = 0

eclipse

Identify the conic section that the given equation represents.x2 − 3xy + 5y2 − 28x + 16y − 30 = 0

eclipse

Identify the standard form of the equation by completing the square. Then identify the conic and its correct graph.9x2 + 16y2 − 126x − 160y + 697 = 0

eclipse <--- and ---> (wider not the longer one)

Graph the equation 9x2 + 4y2 = 36 on a graphing calculator. Identify the conic section. Then identify the center and intercepts for circles and ellipses, or the vertices and direction that the graph opens for parabolas and hyperbolas.

ellipse center: (0, 0) intercepts: (±2, 0), (0, ±3)

Graph the equation 4x2 + 16y2 = 64 on a graphing calculator. Identify the conic section. Then identify the center and intercepts for circles and ellipses, or the vertices and direction that the graph opens for parabolas and hyperbolas.

ellipse center: (0, 0) intercepts: (±4, 0), (0, ±2)

Identify the conic section that the given equation represents. (x-5)^2/81 - 2y^2 =1

hyperbola

Identify the conic section that the given equation represents. (y+7)^2/36 -x^2=1

hyperbola

Identify the conic section that the given equation represents.4x2 − 22xy + 6y2 + 42x − y + 12 = 0

hyperbola

Identify the standard form of the equation by completing the square. Then identify the conic and its correct graph.16x2 − 9y2 − 224x + 90y + 415 = 0

hyperbola (x-7)^2/9 -(y-5)^2/16 =1

Graph the equation x2 − y2 = 169 on a graphing calculator. Identify the conic section. Then identify the center and intercepts for circles and ellipses, or the vertices and direction that the graph opens for parabolas and hyperbolas.

hyperbola vertices: (±13, 0) opens horizontally

Graph the equation x2 − y2 = 49 on a graphing calculator. Identify the conic section. Then identify the center and intercepts for circles and ellipses, or the vertices and direction that the graph opens for parabolas and hyperbolas.

hyperbola vertices: (±7, 0) opens horizontally

Identify the value of p for the parabola. x+11 = 1/18 (y-4)^2

p=4.5

Identify the conic section that the given equation represents. y+1= -1/20(x-2)^2

parabola

Identify the conic section that the given equation represents.9x2 − 12xy + 4y2 + 38x − 60y + 121 = 0

parabola

Graph the equation 7y2 = x on a graphing calculator. Identify the conic section. Then identify the center and intercepts for circles and ellipses, or the vertices and direction that the graph opens for parabolas and hyperbolas.

parabola vertex: (0, 0) opens right

Identify the vertices and co-vertices of the hyperbola.

vertices: (1, −10), (1, 2)co-vertices: (−8, −4), (10, −4)

Identify the vertices and co-vertices of the hyperbola.

vertices: (−5, −2), (11, −2)co-vertices: (3, −6), (3, 2)

Identify the vertices and co-vertices of the hyperbola.

vertices: (−6, −3), (−6, 7)co-vertices: (−9, 2), (−3, 2)

Identify the equation for the parabola with vertex at the origin and directrix x = −2.

x = 1/8 y^2

Identify the equation for the parabola with vertex (0, 0) and directrix x = 2.5.

x= -1/10 y^2

Identify the equation for the parabola with vertex (0, 0) and directrix x = 8.

x= -1/32 y^2

Identify the equation for the parabola with focus F(4, 0) and directrix x = −4.

x= 1/16 y^2

Identify the directrix of the parabola. x-8= - 1/20 (y+2)^2

x=13

Identify the axis of symmetry for the parabola. y+3 = -1/5 (x-4)^2

x=4

Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0).

x^2/169 + y^2/25 =1

Identify an equation in standard form for a hyperbola with center (0, 0), vertex (−5, 0), and focus (−6, 0).

x^2/25 - y^2/11 =1

Identify an equation in standard form for a hyperbola with center (0, 0), vertex (6, 0), and focus (10, 0).

x^2/36 -y^2/64 =1

Identify the asymptotes of the hyperbola.

y + 2 = +_ 4/7 (x-3)

Identify the asymptotes of the hyperbola.

y = +- 9/2 (x+7) + 3

Identify the asymptotes of the hyperbola.

y = +_ 9/11 (x+2) +5

Identify the directix of the parabola. y + 4 = -1/12 (x-5)^2

y = -1

Identify the equation for the parabola with vertex at the origin and directrix y = 3.

y = -1/12 x^2

Identify the equation for the parabola with vertex at the origin and directrix y = 7.

y = -1/28 x^2

Identify the equation for the parabola with focus F(0, −9.5) and directrix y = 9.5.

y = -1/38 x^2

Identify the equation for the parabola with vertex at the origin and directrix y = −3.

y = 1/12 x^2

Identify the equation for the parabola with focus F(0, 6) and directrix y = −6.

y = 1/24 x^2

Identify the directrix of the parabola. y-5=1/16 (x-3)^2

y =1

Identify the equation for the line tangent to the circle x2 + y2 = 25 at the point (−3, −4).

y= -3/4 x - 25/4

Identify the equation for the line tangent to the circle x2 + y2 = 100 at the point (−6, 8).

y= 3/4 x + 25/2

Identify the equation for the line tangent to the circle x2 + y2 = 169 at the point (−5, 12).

y= 5/12 x + 169/12

Identify the axis of symmetry for the parabola. x-8 = -1/20 (y+2)^2

y=-2

Identify an equation in standard form for a hyperbola with center (0, 0), vertex (0, −4), and focus (0, −5).

y^2/ 16 - x^2/9 =1

Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (0, 11), and a co-vertex at (4, 0).

y^2/121 + x^2/16 = 1

Identify an equation in standard form for a hyperbola with center (0, 0), vertex (0, 17), and focus (0, 19).

y^2/289 - x^2/72 = 1

Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (0, 6), and a co-vertex at (2, 0).

y^2/36 + x^2/4 = 1

Identify an equation in standard form for a hyperbola with center (0, 0), vertex (0, 8), and focus (0, 12).

y^2/64 - x^2/80 =1