Question

A hyperbola has vertices (5,0) and (-5,0). Its

Answer 1

Answer:

The equation of the hyperbola   $\frac{x^2}{25} - \frac{y^2}{3696} = 1$

Step-by-step explanation:

Given hyperbola vertices are (5,0) and (-5,0)

The foci of the hyperbola is (61,0) and (- 61,0) so the foci is lie on x-axis

here the vertex a =5 and foci ('c')= 61

we know the condition $c^{2} = a^2+b^2$

  now substitute a =5 and c= 61

                            b^2 = 61^2 - 5^2 = 3696

                            a^2 = 25

The equation of the hyperbola   $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$

The equation of the hyperbola   $\frac{x^2}{25} - \frac{y^2}{3696} = 1$