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The number of distinct normal lines that...

The number of distinct normal lines that can be drawn to the ellipse `(x^2)/(169)+(y^2)/(25)=1` from the point `P(0,6)` is one (b) two (c) three (d) four

A

one

B

two

C

three

D

four

Text Solution

Verified by Experts

`(x^(2))/(169)+ (y^(2))/(25=1`
The equation of normal at the point `(13 cos theta, 5 sin theta)` is `(13x)/(cos theta)-(5y)/(sin theta)=144`
It passes through (0,6). Thereofore, `0-30 =144 sin theta`
`or sin theta=-(5)/(24)`
or `theta=2pi-sin^(-1).((5)/(24)) and pi+sin^(-1).(5)/(24)`
Also, the y-axis is one of the normals.
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