Question

The equation $\frac{x^2}{29-p}+\frac{y^2}{4-p}=1(p\ne 4,29)$ represents -

• A. an ellipse if $p$ is any constant greater than $4$
• B. hyperbola if $p$ is any constant between $4$ and $29$.
• C. a rectanglar hyperbola is $p$ is any constant greater than $29$.
• D. no real curve is $p$ is less than $29$.

Answer 1

The correct option is B hyperbola if $p$ is any constant between $4$ and $29$.

Equation of Hyperbola is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

if p lies between $4$ and $29$ then coefficient of $y^2$ is negative and coefficient of $x^2$ is positive

Hence, it satisfies the equation of Hyperbola between $4$ and $29$