MSTE

𝟒𝟓°

.Determine the angle of rotation such that the transformed equation of xy = 1 will have no x'y' term.

x′𝟐 − 𝐲 ′𝟐 = �

.Determine the new equation of the curve xy = 4 when the axes are rotated 45°.

y′𝟐 = 𝟔𝐱 ′

.Determine the new equation of the parabola y 2 − 6x + 4y + 22 = 0 if the origin is translated to its vertex.

𝟑𝟎°

.Find the acute angle of rotation such that the transformed equation of 7x 2 + √3xy + 6y 2 = 16 will have no x'y' term.

𝟐𝐜 = 𝟐√5

.Find the distance between foci of the curve 9x 2 + 4y 2 − 36x − 8y + 4 = 0.

𝟑𝐱𝟐 − 𝐲𝟐 − 𝟐𝟎𝐱 + 𝟔𝐲 + 𝟐𝟑 = 0

.Find the locus of points such that the distance from (2, 3) to any point on the curve is twice the distance from the line x = 3 to that point on the curve.

2𝟓(𝐱 ′ ) 𝟐 + 𝟑𝟔(𝐲 ′ ) 𝟐 = 𝟗𝟎𝟎

.Find the new equation of the curve (x−4)2/36 + (y−3)2/25 = 1 if the origin is translated to the center of the ellipse

(𝟏, − 𝟏/𝟐 )

.Find the point to which the origin must be translated in order that the transformed equation of the curve 4x 2 + 4y 2 − 8x + 4y + 1 = 0 will have no first-degree term.

R = √𝟒6

.Find the radius of the sphere x 2 + y 2 + z 2 + 2x − 6y − 12z = 0.

√𝟏𝟑/2

.The eccentricity of the curve 9x 2 − 4y 2 = 36 is?

𝟐𝐱 ′𝐲 ′ + 𝟐𝟓 = 0

.Transform the equation x 2 − y 2 = 25 by rotating the axes through 45°.

(𝐱 − 𝟐) 𝟐 + (𝐲 − 𝟑) 𝟐 = 𝟐5

A circle passes through the point (5, 7) and has its center at (2, 3). Find its equation

L𝐑 = 4

A parabola has an equation of x 2 − 4y − 2x + 8 = 0. Find the length of the latus rectum.

(𝐲 − 𝟒) 𝟐 = 𝟖(𝐱 − 𝟐)

A parabola has its vertex at (2,4) and focus at (4,4). Determine its equation

5𝐱 − 𝟐𝐲 = 0

What is the equation of the line that passes through the origin and parallel to the line 5x - 2y + 3 = 0?

4𝐱 + 𝟑𝐲 = 𝟎

What is the equation of the line that passes through the origin and perpendicular to the line 3x - 4y + 3 = 0?

y = 𝟑𝐱 + 𝟓

What is the equation of the line with slope equal to 3 and y-intercept of 5?

(𝟑 + 𝟐√𝟑)𝐱 ′ + (𝟐 − 𝟑√𝟑)𝐲 ′ = 2

What is the new equation of the line 3x + 2y = 1 if the axes are rotated 60°?

𝐫 = √𝟒𝟔

What is the radius of a sphere that passes through (1, 3, 6) and has its center at the origin?

r=6

What is the radius of the curve x 2 + y 2 − 6x − 8y − 11 = 0?

6x ± 𝟕𝐲 = 0

determine the equation of the asymptote of the hyperbola x2/49 − y2/36 = 1.

𝐀 = 𝟐

Two lines 3x + 2y - 3 = 0 and Ax - 3y +2 = 0 are perpendicular to each other. Determine the value of A

𝛉 = 𝟓𝟒. 𝟏𝟔𝟐°

What is the acute angle formed between the lines 4x - y + 3 = 0 and 2x - 5y - 1 = 0?

C(2,-1)

The curve x 2 + y 2 − 4x + 2y − 4 = 0 has its center at?

always equal to 1.

The eccentricity of a parabola is always equal to?

4𝐱 − 𝟑𝐲 + 𝟒 = 0

The equation of the line passing through points (2,4) and (5,8) is?

d = 0.743

What is the distance between the lines: 5x - 2y + 3 = 0 and 5x - 2y + 7 = 0?

e = 𝟑/5

What is the eccentricity of an ellipse whose length of major and minor axes equal to 5 and 4, respectively, with center at origin?

𝛉 = 𝟒𝟓°

Compute for the acute angle between the lines whose slopes are, m1 = 1/3 and m2 = 2.

x 𝟐 + 𝐲 𝟐 − 𝟑𝐱 = 0

Convert r = 3cosθ into Cartesian coordinates.

𝐫 − 𝟐 𝐜𝐨𝐬 𝛉 + 𝟒 𝐬𝐢𝐧 𝛉 = 0

Convert x 2 + y 2 − 2x + 4y = 0 into polar form

(𝟏𝟎. 𝟑𝟗𝟐,𝟔)

Determine the Cartesian coordinate of a point having a polar coordinate of (12, 30°).

C (−𝟒, −𝟑, −𝟓)

Determine the center of the sphere x 2 + y 2 + z 2 + 8x + 6y + 10z = 0.

x = −4

Determine the equation of the directrix of the parabola: y 2 = 16x

𝐟 = 𝟏/2

Determine the flatness of the ellipse 9x 2 + 4y 2 − 36x − 8y + 4 = 0

(𝟐,𝟑, 𝟒)

Determine the point of intersection of the planes: 4x − 3y + 2z = 7, x + 2y − z = 4 and 5x + y + 2z = 21.

5∠𝟓𝟑. 𝟏𝟑°

Determine the polar coordinates of a point having a Cartesian coordinate of (3,4).

A = 𝟐𝟖 𝐬𝐪. 𝐮𝐧𝐢𝐭s

Find the area of the triangle whose vertices are at points A (3, 4), B (-2, 1) and C (5, -6).

C(𝟏, −𝟏)

Find the centroid of the triangle whose vertices are at points (3, 4), (6, -9) and (-6, 2).

𝐝 = √𝟓9

Find the distance between points (2, 3, 5) and (-1, 4, -2) in space

d = √89

Find the distance between the points A (-2, 3) and B (6, 8).

5𝐱 ′ − 𝟐𝐲 ′ + 𝟏𝟒 = 0

Find the new equation of the curve 5x - 2y = 2 if the origin is translated to the point (2, -3).

𝟑𝐱 ′𝟐 − 𝟐√𝟑𝐱 ′𝐲 ′ + 𝐲 ′𝟐 = 𝟑𝟐𝐱 ′ + 𝟑𝟐√𝟑𝐲′

Find the new equation of the curve x 2 = 16y if the axes are rotated 30°

√𝟓/𝟐

Find the second eccentricity of the curve 9x 2 + 4y 2 − 36x − 8y + 4 = 0.

d = 𝟏. 𝟗4

Find the shortest distance from point (2, 3) to the line 3x + 2y - 5 = 0

𝐦 = 𝟑/𝟐

Find the slope of the line 3x - 2y + 3 = 0.

V(−𝟏, 𝟐)

Find the vertex of the parabola whose equation is y 2 − 2x − 4y + 2 = 0.

𝐡 = 3

How far is the center of the circle x 2 + y 2 − 6x − 8y − 11 = 0 from the yaxis?