1.Write the equation of the conic section with the given properties:

Question

A hyperbola with vertices(0,6)(0,-6)and asymptotes y=3/4x and y=-3/4x.
2.Write the equation of the conic section with the given properties:
An ellipse with vertices(0,-5)(0,5)and a minor axis of length 8.
Im having major trouble i got x^2=4r2 for 1 and x^2=49 for 2

Answer 1

#1. vertices indicate you have a vertical axis of symmetry. So, since the foci are evenly spaced from (0,0),

y^2/a^2 - x^2/b^2 = 1

The vertices are at y = ±6, so

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

The asymptotes are y = ±(b/a)x, so b/a = 3/4, or b=8

see the info at

http://www.wolframalpha.com/input/?i=hyperbola+y^2%2F36+-+x^2%2F64+%3D+1

The ellipse is similar. The semi-major axis is a=5, the semi-minor axis is b=4. Since the vertices are in the y-axis, equidistant from (0,0),

x^2/16 + y^2/25 = 1

See

http://www.wolframalpha.com/input/?i=ellipse+x^2%2F16+%2B+y^2%2F25+%3D+1

I have no idea how you got your results. They are in no way the equations of conic sections. You have some serious reviewing to do.