Web Analytics

Verified Answer :

THe hyperbola is horizontally oriented.

c^2 = a^2 + b^2

34 = 9 + b^2

b^2 = 25

b = 5

x^2/9 - y^2/25 = 1

I hope that this is the answer that you were looking for and it has helped you.

Answer:

\(\frac{x^2}{9}-\frac{b^2}{25}=1\)

Step-by-step explanation:

Since, we know that,

The equation of hyperbola,

\(\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\)

Where, (h,k) is the center of the hyperbola,

Here, h = k = 0,

So, the equation of hyperbola is,

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

Also, a = distance between center and vertices of hyperbola,

Given, vertices = (±3,0)

\(a=\sqrt{(0-3)^2+(0-0)^2}=\sqrt{9}=3\)

\(\implies a^2 = 9\)

Now, foci, c= (±√34,0),

Since, foci of hyperbola (1) is,

\((\pm\sqrt{a^2+b^2},0)\)

\(\implies a^2+b^2= (\sqrt{34})^2\)

\(\implies 3^2 + b^2 = 34\)

\(\implies b^2 = 34 - 9 = 25\)

Hence, the equation of the given hyperbola is,

\(\frac{x^2}{9}-\frac{b^2}{25}=1\)

Related Questions