Conics Problem Part 2: Formulas and Solutions | Homework Statement

[temaire]

Homework Statement

This is the second page.

http://img116.imageshack.us/img116/7519/arch2iq9.jpg​

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Homework Equations

Formulas on picture above.

The Attempt at a Solution

I'am just wondering if everything looks fine.

 

[konthelion]

part (i) is correct.
For part (ii), I don't think that's how you would solve for b. There's a formula to solve for b. b^2=c^2-a^2 where c is your focii and a is the distance from your center (0,30) to the vertex of the hyperbola. a=10, c=30, then b=?

 

[konthelion]

Whoops, I realized that the problem is using a different form of the vertical hyperbola instead of \frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1, so in this case I switched a and b around.

In this problem, where b=10(the distance from center to vertex of hyperbola) is correct.