multiple choice pre calc

19 questions only a couple not multiple choice and one needing a graph  

Question 1 of 20

5.0 Points

Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -5 and 5

A.X^2/4+Y^2/25=1

B.X^2/4+Y^2/21=1

C.X^2/25+Y^2/21=1

D.X^2/21+Y^2/25=1

Question 2 of 20

5.0 Points

Convert the equation to the standard form for a hyperbola by completing the square on x and y.

y2 – 25×2 + 4y + 50x – 46 = 0

A.(Y+4)^2/25-(X-2)^2=1

B.(X+2)^2/25-(Y-1)^2=1

C.(X-1)^2-(X+2)^2/25=1

D.(X+2)^2/25-(X-1)^2=1

Question 3 of 20

5.0 Points

Write the equation in terms of a rotated x’y’-system using θ, the angle of rotation. Write the equation involving x’ and y’ in standard form. xy +16 = 0; θ = 45°

A.X’^2/4+Y’^2=1

B.Y’^2=-32X’

C.Y’^2/32+X’^2/32=1

D.Y’^2/32-X’^2/32=1

Question 4 of 20

5.0 Points

Match the equation to the graph.

x2 = 7y

Question 5 of 20

5.0 Points

Sketch the plane curve represented by the given parametric equations. Then use interval notation to give the relation’s domain and range.

x = 2t, y = t2 + t + 3

A. Domain: (-∞, ∞); Range: -1x, ∞)

B. Domain: (-∞, ∞); Range: [ 2.75, ∞)

C. Domain: (-∞, ∞); Range: [ 3, ∞)

D. Domain: (-∞, ∞); Range: [ 2.75, ∞)

Question 6 of 20

5.0 Points

Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.

y = ± SQRT x^2-5

A. Asymptotes: y = ± x

B. Asymptotes: y = ±5/3 x

C. Asymptotes: y = ±3/5 x

D.Asymptotes: y = ± x

Question 7 of 20

5.0 Points

Find the vertices and locate the foci for the hyperbola whose equation is given.

49×2 – 100y2 = 4900

A.vertices: ( -10, 0), ( 10, 0)

foci: (√-51 , 0), ( √51 , 0

B. vertices: ( -10, 0), ( 10, 0)

foci: (-√149 , 0), ( √149, 0)

C. vertices: ( -7, 0), ( 7, 0)

foci: (- √149, 0), (√149 , 0)

D. vertices: (0, -10), (0, 10)

foci: (0, -√149 ), (0,√149 )

Question 8 of 20

5.0 Points

Use the center, vertices, and asymptotes to graph the hyperbola.

(x – 1)2 – 9(y – 2)2 = 9

(what would the graph look like? )

Question 9 of 20

5.0 Points

Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations.

x = 6 cos t, y = 6 sin t; 0 ≤ t ≤ 2π

A. x2 – y2 = 6; -6 ≤ x ≤ 6

B. x2 – y2 = 36; -6 ≤ x ≤ 6

C. x2 + y2 = 6; -6 ≤ x ≤ 6

D. x2 + y2 = 36; -6 ≤ x ≤ 6

Question 10 of 20

5.0 Points

Graph the ellipse.

16(x – 1)2 + 9(y + 2)2 = 144

i need a graph

Rewrite the equation in a rotated x’y’-system without an x’y’ term. Express the equation involving x’ and y’ in the standard form of a conic section.

31×2 + 10√3xy + 21y2 -144 = 0

A. x’2 = -4√2 y’

B. y’2 = -4√2x’

C. x’^2/4+y’^2/9+=1

D. x’^2/9+y’^2/4=1

12-

Question 13 of 20

5.0 Points

Is the relation a function?

y = x2 + 12x + 31

A. Yes

B. No

Question 14 of 20

5.0 Points

y2 = -2x

what would this graph look like ?

Question 15 of 20

5.0 Points

Find the location of the center, vertices, and foci for the hyperbola described by the equation.

(x+4)^2/36-(y-1)^2/25=1

no multiple choice.

Question 16 of 20

5.0 Points

Determine the direction in which the parabola opens, and the vertex.

y2 = + 6x + 14

A. Opens upward; ( -3, 5)

B. Opens upward; ( 3, 5)

C. Opens to the right; ( 5, 3)

D. Opens to the right; ( 5, -3)

Question 17 of 20

5.0 Points

Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.

y2 + 2y – 2x – 3 = 0

A. (y + 1)2 = 2(x + 2)

B. (y – 1)2 = -2(x + 2)

C. (y + 1)2 = 2(x – 2)

D. (y – 1)2 = 2(x + 2)

Question 18 of 20

5.0 Points

Write the appropriate rotation formulas so that in a rotated system the equation has no x’y’-term.

10×2 – 4xy + 6y2 – 8x + 8y = 0

A. x = -y’; y = x’

B. x=√2-√2/2x’-√2+√2/2y’; y=√2+√2/2x’+√2-√2/2y’

C. x=√2/2(x’-y’); Y=√2/2(x’+y’)

D. x+=1/2x’-√3/2y’; y=√3/2x’+1/2y’

Question 19 of 20

5.0 Points

Halley’s comet has an elliptical orbit with the sun at one focus. Its orbit shown below is given approximately by r=10.71/1+0.883sin⊖ In the formula, r is measured in astronomical units. (One astronomical unit is the average distance from Earth to the sun, approximately 93 million miles.) Find the distance from Halley’s comet to the sun at its greatest distance from the sun. Round to the nearest hundredth of an astronomical unit and the nearest million miles.

A. 12.13 astronomical units; 1128 million miles

B. 91.54 astronomical units; 8513 million miles

C. 5.69 astronomical units; 529 million miles

D. 6.06 astronomical units; 564 million miles

Convert the equation to the standard form for a hyperbola by completing the square on x and y.

x2 – y2 + 6x – 4y + 4 = 0

A. (x + 3)2 + (y + 2)2 = 1

B. (y+3)^2/16-(x+2)^2/36=1

C. (x + 3)2 – (y + 2)2 = 1

D. (y + 3)2- (x + 2)2 = 1