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Question

The length of the latusrectum of a conic is 2. Its focus is (1,1) and its directrix is 3x4y+2=0 then the conic is

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

The correct option is A a parabola
Distance between the focus (1,1) and directrix is 3(1)4(1)+225=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.

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