Question

What is the equation of the hyperbola with foci (0, 10), (0, ?10) and vertices (0, 6), (0, ?6)

Answer 1

As given,

Foci (0,10) ; (0,-10) and Vertices (0,6) ; (0,-6)

Now we know the general equation of hyperbola will be,

$\frac{y^{2} }{a^{2} } -\frac{x^{2} }{b^{2} } =1$

Now distance from origin to vertex is given, 6 ;

therefore, $a=6$

And distance from origin to Focus is given , $c=10;$

Using the equation, $c^{2}=a^{2}+b^{2} \\c=10 ; a=6,$

Apply these values in the equation and find out the value of b,

$c^{2}=a^{2} +b^{2}\\10^{2}=6^{2}+b^{2}\\100=36+b^{2}\\100-36=b^{2}\\ b^{2}=64\\ b=8$

Hence equation of Hyperbola will be,

$\frac{y^{2} }{6^{2} }-\frac{x^{2} }{8^{2} }=1\\\frac{y^{2} }{36}-\frac{x^{2} }{64} =1$

Here we are done.

Answer 2

Answer:

y^2/36 - x^2/64 = 1

Hope this helps <3