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Question

Let the line y=mx and the ellipse 2x2+y2=1 intersect at point P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at (132,0) and (0,β), then β is equal to:

A
23
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B
23
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C
223
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D
23
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Solution

The correct option is D 23

Let P(x1,y1)
Given equation of ellipse is 2x2+y2=1

Equation of normal at P(x1,y1) is
x2x1yy1=12
It passes through (132,0)
x1=132
using ellipse equation
y1=223 as P lies in first quadrant.

Since (0,β) lies on the normal of the ellipse at point P, hence we get
3β22=12β=23

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