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Question

The equations of the tangents to the ellipse x2+16y2=16, each one of which makes an angle of 60 with the xaxis, is

A
y=3x±1
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B
y=3x±3
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C
y=3x±5
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D
y=3x±7
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Solution

The correct option is D y=3x±7
We have, x2+16y2=16
x242+y212=1
This is of the form x2a2+y2b2=1, where a2=16 and b2=1
So, the equation of the tangents with slope m are
y=mx±a2m2+b2 (1)
Given, m=tan60
m=3
From equation (1), we get
y=3x±16×3+1
y=3x±7

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