Need help with Conic Sections!! Will give medal! Question in comments. Please any help is appreciated.

Question

ohmybookness · Answer

I solved everything else I just need to solve #6-10. 

it says to solve it algebraically
& 
to use a graph to demonstrate that my answers are correct. 

I believe I already have a graph I just need help solving them algebraically.

ohmybookness · Answer

attachment

ohmybookness · Answer

@ckylee can you help me here?

ohmybookness · Answer

@ganeshie8 can you help me with these questions?

anonymous · Answer

For #6,
First use elimination to find x and y values
$$32x^2 + 9y^2 = 324$$$$3y^2 - x^2 = 3$$
$$32x^2 + 9y^2 = 324$$$$-3x^2 + 9y^2 = 9$$
$$35x^2 = 315$$
$$x^2 = 9$$$$x = \pm3$$$$y= \pm2$$ (plug x=3 to any equation to get y)

Therefore there are combinations of (3,2), (3, -2), (-3, 2) and (-3,-2).

anonymous · Answer

I'm not sure about conic sections (ellipses and circles) though. Trigonometry isn't my strongest area :P