If an ellipse has foci (±2,0) and vertices (±3,0), locate the vertices of its mi

Question

If an ellipse has foci (±2,0) and vertices (±3,0), locate the vertices of its minor axis.      A. B. C. D.

   Where are the foci of the hyperbola ?

     A. (0,±4,) B. (0,±2) C. (±2,0) D. (±4,0) 4.   The eccentricity e tells you which of the following things about a conic section in polar coordinates?      A. Whether it can be parameterized B. Its orientation with respect to the pole C. How far its focus is from its directrix D. Which type of conic section it is What kind of conic section is 6x2 + 9xy 3y2 + 11x 6y + 1 = 0?      A. Parabola B. Hyperbola C. Ellipse D. Circle
If the conic section Ax2 + Cy2Dx + Ey + F = 0 has A = C, then it's which of the following shapes?      A. A hyperbola B. A circle C. A parabola D. An ellipse   What is a parameterized version of the curve given by y 3 = x + sin x?      A. t = x, sinx y + 3 B. t = 3 = y, t + sint = x C. x = t, y = t + sint + 3 D. y = 3t, x = y + sint When is it possible to eliminate the parameter from a set of parametric equations?      A. When you have the original non-parametric form given B. When you can isolate the parameter in one equation C. Only when one equation is linear D. Always Convert the equation of the ellipse 5x2 + 6y 2 10x 25 = 0 to standard form.      A. B. 5(x 1)2 + 6y 2 = 30 C. D. The equation isn't that of an ellipse.
Express the parametric equations without the parameter.      A. B. C. D.

Explanation / Answer

1)centre =(0,0)

a =3 , ae =2

ae/a =2/3

e =2/3

e=(1-(b/a)2)

(1-(b/3)2) =2/3

(1-(b/3)2)=4/9

(b/3)2=1-(4/9)

(b/3)2=5/9

b/3=(5)/3

b=5

vertices of minor axis =(0,b),(0,-b)

vertices of minor axis =(0,5),(0,-5)

2)a2=6,b2=10

e=(1+(b/a)2)

e=(1+(10/6))

e=4/6

ae =4

focie = (ae,0),(-ae,0)

focie=(4,0),(-4,0)

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