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Question

Tangents are drawn through the point (4,3) to the ellipse x216+y29=1. The points at which these tangents touch the ellipse are

A
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B
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C
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D
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Solution

The correct option is A
Let P(x1,y1) be the point of contact.
The equation of the tangent at P is xx116+yy19=1
If this tangent passes through (4,3), then x14+y133=1y133=1x14y1=12333x14
P lies on the ellipse x2116+y219=1x2116+(12333x1)2144=1x21+(433x1)2=16
x21+48+3x2124x1=164x2124x1+32=0x216x1+8=0x1=2or4
x1=2y1=332,x1=4y1=0
The required points are (2,332),(4,0)

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