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Question

The equation of the latus rectum of a parabola is x+y=8 and the equation of the tangent at the vertex is x+y=12. Then the length of the latus rectum is

A
42 units
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B
22 units
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C
8 units
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D
82 units
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Solution

The correct option is D 82 units
Since, x+y=8 and x+y=12 are parallel.
Therefore, distance between them is,
AS=C1C2a2+b2=42=22

Hence, length of the latus rectum is,
LR=4AS
=4×22
=82 units

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