Analytic Geometry (solve)

Given the triangle with vertices at A(1,4), B(9,6), and C(7,2). Find the: terminal point if side AC is extended three times its own length a.(24,-6) b.(25,-4) c. (24,-5) d. (25,-3)

A

Given the triangle with vertices at A(1,4), B(9,6), and C(7,2). Find the: distance from C to side AB a.3.4 b.4.3 c. 4.0 d. 3.7

A

What is the radius of a circle with the equation2𝑥2+2𝑦2−3𝑥+4𝑦−1=0?a.√33/4 c. √33/3 b.33/16 d. 32/15

A

A circle has the equation𝑥2+𝑦2−4𝑥+6𝑦−12=0. Find the: farthest distance from the point (5,6) to the circle a.14.2 units c. 15.4 units b.14.5 units d. 15.2 units

B

Given the triangle with vertices at A(1,4), B(9,6), and C(7,2). Find the: angle C of the triangle a.98.1° b.89.8° c. 81.9° d. 91.1°

B

Given the triangle with vertices at A(1,4), B(9,6), and C(7,2). Find the: equation of the line through side AB a.𝑥+4𝑦+15=0 b.𝑥−4𝑦+15=0 c. 𝑥+4𝑦−15=0 d. 𝑥−4𝑦−15=0

B

A circle has the equation𝑥2+𝑦2−4𝑥+6𝑦−12=0. Find the: center of the circle a.(-2,3) c. (2,-3) b.(-3,2) d. (3,-2)

C

Given the triangle with vertices at A(1,4), B(9,6), and C(7,2). Find the: distance from 𝑥−4𝑦−12=0 to side AB a.5.66 b.5.33 c. 6.55 d. 6.88

C

Given the triangle with vertices at A(1,4), B(9,6), and C(7,2). Find the: equation of the perpendicular bisector of side BC a.𝑥−𝑦−8=0 b.𝑥−2𝑦+8=0 c.𝑥+2𝑦−16=0 d. 𝑥+𝑦+16=0

C

Situation 1.For problems 1-9, refer here. Given the triangle with vertices at A(1,4), B(9,6), and C(7,2). Find the: point of intersection of the medians a.(14/3, 3) c. (17/3, 4) b.(15/3, 4) d. (16/3, 3)

C

A circle has the equation𝑥2+𝑦2−4𝑥+6𝑦−12=0. Find the: nearest distance from the point (5,6) to the circle a.5.4 units c. 4.2 units b.5.2 units d. 4.5 units

D

Find the equation of the circle circumscribing the triangle with vertices at P(-1,-4), Q(3,-2), and R(5,2). a.𝑥2+𝑦2+4𝑥+6𝑦−37=0 b.𝑥2+𝑦2−4𝑥−6𝑦+37=0 c.𝑥2+𝑦2−4𝑥+6𝑦+37=0 d.𝑥2+𝑦2+4𝑥−6𝑦−37=0

D

Given the triangle with vertices at A(1,4), B(9,6), and C(7,2). Find the: equation of the line through (0,-3) and parallel to side AB a.𝑥+4𝑦+12=0 b.𝑥−4𝑦+12=0 c. 𝑥+4𝑦−12=0 d. 𝑥−4𝑦−12=0

D

Situation 1.For problems 1-9, refer here. Given the triangle with vertices at A(1,4), B(9,6), and C(7,2). Find the: area of the triangle a.15 sq. units b.12 sq. units c. 13 sq. units d. 14 sq. units

D

An automobile headlight has a parabolic reflector that is 6 inches in diameter and 3 inches deep. How far from the vertex should the light bulb be placed? a. 0.75" c. 1.00" b. 0.50" d. 0.88"

a

Curve 16𝑥^2−9𝑦^2−64𝑥−72𝑦−224=0 equation of the upward asymptote a.4𝑥−3𝑦−20=0 c. 4𝑥−3𝑦−4=0 b.4𝑥+3𝑦−20=0 d. 4𝑥+3𝑦+4=0

a

Curve 16𝑥^2−9𝑦^2−64𝑥−72𝑦−224=0 length of latus rectum a.10.7 units c. 6.4 units b.16.7 units d. 4.5 units

a

Curve 16𝑥^2−9𝑦^2−64𝑥−72𝑦−224=0 vertices a.(-1,-4) & (5,-4) c. (-1,-7) & (5,-1) b.(2,0) & (2,-8) d. (-3,-4) & (7,-4)

a

Given a curve whose equation is 9𝑥2+25𝑦2+54𝑥−100𝑦−44=0. Find: its perimeter a.25.9 units c. 26.4 units b.25.4 units d. 26.9 units

a

Given a parabola whose equation is 𝑥2+2𝑥−4𝑦+9=0, find the following: vertex a.(-1,2) c. (-2,1) b.(1,-2) d. (2,-1)

a

Curve 16𝑥^2−9𝑦^2−64𝑥−72𝑦−224=0 center a.(2,4) c. (-2,4) b.(2,-4) d. (-2,-4)

b

Given a curve whose equation is 9𝑥2+25𝑦2+54𝑥−100𝑦−44=0. Find: its area a.12πsq. units c. 18πsq. units b.15πsq. units d. 9πsq. units

b

Given a curve whose equation is 9𝑥2+25𝑦2+54𝑥−100𝑦−44=0. Find: its center a.(-2,3) c. (2,-3) b.(-3,2) d. (3,-2)

b

Given a curve whose equation is 9𝑥^2+25𝑦^2+54𝑥−100𝑦−44=0. Find: its foci a.(-6,2) & (0,2) c. (-8,2) & (2,2) b.(-7,2) & (1,2) d. (-3,6) & (-3,-2)

b

Given a parabola whose equation is 𝑥2+2𝑥−4𝑦+9=0, find the following: equation of the axis of symmetry a.𝑥=1 c. 𝑦=3 b.𝑥=-1 d. 𝑦=2

b

The distance between points (5,30°) &(-8,-50°) is: a.9.84 c. 10.04 b.10.14 d. 9.94

b

What is the distance between the vertices of the ellipse: 64𝑥^2+25𝑦^2+16𝑥−16𝑦−648=0? a.5.11 c. 12.54 b.10.21 d. 6.27

b

Find the volume of the tetrahedron bounded by the coordinate planes and the plane 8𝑥+12𝑦+4𝑧−24=0. a.5 cubic units c. 6 cubic units b.9 cubic units d. 12 cubic units

c

Given a curve whose equation is 9𝑥2+25𝑦2+54𝑥−100𝑦−44=0. Find: its vertices a.(-6,2) & (0,2) c. (-8,2) & (2,2) b.(-3,7) & (-3,-3) d. (-3,5) & (-3,-1)

c

Given a curve whose equation is 9𝑥2+25𝑦2+54𝑥−100𝑦−44=0. Find: the equation of the directrices a.𝑥=25/4 & 𝑥=13/4 c. 𝑥=−37/4 & 𝑥=13/4 b.𝑥=−37/4 & 𝑥=−25/4 d. 𝑥=37/4 & 𝑥=−13/4

c

Given a parabola whose equation is 𝑥2+2𝑥−4𝑦+9=0, find the following: equation of directrix a.𝑥=1 c. 𝑦=1 b.𝑦=3 d. 𝑥=3

c

Given a parabola whose equation is 𝑥2+2𝑥−4𝑦+9=0, find the following: length of latus rectum a.1 unit c. 4 units b.8 units d. 2 units

c

Points C (5,7,z) and D (4,1,6) are 7.28 units apart. Find the value of z. a.-2 or 10 c. 2 or 10 b.-2 or -10 d. 2 or -10

c

What is the vertex of the curve2𝑦2+2𝑥+5𝑦+7=0? a. (−5/4,−31/16) c. (−31/16,−5/4) b. (31/16,5/4) d. (5/4,31/16)

c

7.Find the equation of the parabola with vertex at (4,3) and focus at (4,-1). a.𝑦2−8𝑥+16𝑦−25=0 b.𝑦2+8𝑥−16𝑦−25=0 c.𝑥2+8𝑥−16𝑦+32=0 d.𝑥2−8𝑥+16𝑦−32=0

d

Curve 16𝑥^2−9𝑦^2−64𝑥−72𝑦−224=0 equation of the downward asymptote a.4𝑥−3𝑦−20=0 c. 4𝑥−3𝑦−4=0 b.4𝑥+3𝑦−20=0 d. 4𝑥+3𝑦+4=0

d

Curve 16𝑥^2−9𝑦^2−64𝑥−72𝑦−224=0 foci a.(-1,-4) & (5,-4) c. (-1,-7) & (5,-1) b.(2,0) & (2,-8) d. (-3,-4) & (7,-4)

d

Curve 16𝑥^2−9𝑦^2−64𝑥−72𝑦−224=0 transverse axis and conjugate axis, respectively a.4 & 3 c. 3 & 4 b.8 & 6 d. 6 & 8

d

Find the eccentricity of the curve represented by the parametric equations 𝑥=3cosθand𝑦=4sinθ. a.1.34 c. 0.89 b.0.75 d. 0.66

d

Find the equation of the curve whose center is at (1,0) with one focus at (1,√13). The eccentricity of the curve is √13/2. a.9𝑥2−4𝑦2−8𝑥+15=0 b.4𝑥2−9𝑦2+8𝑥+24=0 c.4𝑦2−9𝑥2+8𝑦−23=0 d.4𝑥2−9𝑦2−8𝑥+40=0

d

Find the length of the curve 𝑟=4sinθ. a.10.23 units c. 9.42 units b.11.68units d. 12.57units

d

Given a curve whose equation is 9𝑥2+25𝑦2+54𝑥−100𝑦−44=0. Find: the length of latus rectum a.6.4units c. 5.7units b.4.5units d. 3.6units

d

Given a parabola whose equation is 𝑥2+2𝑥−4𝑦+9=0, find the following: focus a.(-2,2) c. (0,2) b.(-1,1) d. (-1,3)

d

The polar form of the equation 3𝑥2+2𝑦2=8i s: a.𝑟^2=8 c. 𝑟=8 b.𝑟=8/(cos2θ+2) d. 𝑟^2=8/(cos2θ+2)

d

A circle has the equation𝑥2+𝑦2−4𝑥+6𝑦−12=0. Find the: angent distance from the point (5,6) to the circle a.8.1units c. 8.6units b.9.6units d. 9.1units

A

A circle has the equation𝑥2+𝑦2−4𝑥+6𝑦−12=0. Find the: area of the circle a.78.5 sq. units c. 75.8 sq. units b.87.5 sq. units d. 85.7 sq. units

A