Q. 12. - Calculus

Question

The directrices of the hyperbola with equation $\frac{y^2}{B^2}-\frac{x^2}{A^2}=1$are the lines with equations $x=\pm \frac{A}{e}$, where e is the eccentricity of the hyperbola. What are the equations for the directrices of the hyperbola with equation $\frac{y^2}{B^2}-\frac{x^2}{A^2}=1$

Step-by-Step Solution

Answer

The required answer $y=\frac{B}{e},y=-\frac{B}{e}$where $e$is the eccentricity of the hyperbola.

Step 1: Given information

The given hyperbola is $\frac{y^2}{B^2}-\frac{x^2}{A^2}=1$

Step 2: The objective is to write the directrices of the hyperbola.

A hyperbola is a set of points in a plane whose distances to two fixed points in the plane have a constant difference. It is a curve with two distinct and similar branches.

Every hyperbola has two directrices.

The directrices of the hyperbola $\frac{y^2}{B^2}-\frac{x^2}{A^2}=1$are the horizontal lines.

They are $y=\frac{B}{e}$and $y=-\frac{B}{e}$where $e$is the eccentricity of the hyperbola.