Question

The length of the latus rectum of a conic is $5$. 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 circle

Answer 1

The correct option is C a hyperbola

Length of latus rectum $=5$
Focus $=(-1,1)$
The equation of directrix is $3x-4y+2=0$
Distance of focus from directrix $=\frac{|-3-4+2|}{5}=1$
We can see that, $\text{Length of}LR>2\left(\text{distance between focus and directrix}\right)$
Therefore the conic is a hyperbola.