Question

Equation of the hyperbola with vertices at $(\pm 5,0)$ and foci at $(\pm 7,0)$ is

• A. $24x^2-25y^2=600$
• B. $25x^2-24y^2=600$
• C. $\frac{x^2}{25}-\frac{y^2}{24}=1$
• D. $\frac{x^2}{24}-\frac{y^2}{25}=1$

Answer 1

Answer: (A), (C)

The correct options are
A $24x^2-25y^2=600$
C $\frac{x^2}{25}-\frac{y^2}{24}=1$

$Vertices(\pm 5,0)Foci(\pm 7,0)$

$a=\pm 5$ and $ae=\pm 7$

And $e=\frac{7}{5}$

We know $e=\sqrt{1+\frac{b^2}{a^2}}$

On squaring both sides we get:

$e^2=1+\frac{b^2}{a^2}$

Or $\frac{49}{25}=1+\frac{b^2}{25}$

Or $\frac{b^2}{25}=\frac{24}{25}$

$b^2=24$

The equation of hyperbola is

$\frac{x^2}{25}-\frac{y^2}{24}=1$

$24x^2-25y^2=600$

Hence, Option [A] and [C] are correct.