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Question

The slopes of the tangents drawn from (4,1) to the ellipse x2+2y2=6 are?

A
1,1/5
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B
1,1/5
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C
1.1/5
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D
1,1/5
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Solution

The correct option is D 1,1/5
Equation of ellipse,

x2+2y2=6

Point =(4,1)
Tangent to an ellipse is,

y=mx±a2m2+b2

We have x=4,y=1

a=6,b=3

Put the values
1=4m+6m2+3
(14m)2=6m2+3
1+16m28m=6m2+3
10m28m2=0

5m24m1=0
m=1,1/5

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