Question

The length of the latusrectum of a conic is $2$. Its focus is $(-1,1)$ and its directrix is $3x-4y+2=0$ then the conic is

• A. a parabola
• B. an ellipse
• C. a hyperbola
• D. a. R.H

Answer 1

The correct option is A a parabola

Distance between the focus $(-1,1)$ and directrix is $|\frac{3(-1)-4\left(1\right)+2}{\sqrt{25}}|=1$

It's given that the length of the latus rectum is $2$ which is the double of the distance between the focus $(-1,1)$ and directrix.

In a parabola, the distance of the latus rectum is double of the distance between focus and directrix, therefore, the given conic is a parabola.