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Question

Two tangents on a parabola are xy=0 and x+y=0. Let (2,3) is the focus of the parabola, then

A
The equation of the tangent at vertex is 4x6y+5=0
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B
The equation of the tangent at vertex is 4x6y+1=0
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C
The length of the latus rectum of the parabola is 1052
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D
The length of the latus rectum of the parabola is 1013
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Solution

The correct options are
A The equation of the tangent at vertex is 4x6y+5=0
D The length of the latus rectum of the parabola is 1013
The foot of the perpendicular from the focus upon any tangent lies on the tangent at the vertex.


The foot of perpendicular of (2,3) on the line xy=0 is A(52,52).
The foot of of perpendicular of (2,3) on the line x+y=0 is B(12,12).

The equation of tangent at vertex (Eq. of AB) is 4x6y+5=0

Let the length of the latus rectum be 4a
Then the length of perpendicular to the tangent at vertex from the focus is a.

a=|4(2)6(3)+5|524a=1013

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