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The slopes of the common tangents of the...

The slopes of the common tangents of the ellipse `(x^2)/4+(y^2)/1=1` and the circle `x^2+y^2=3` are `+-1` (b) `+-sqrt(2)` (c) `+-sqrt(3)` (d) none of these

A

`+-1`

B

`+-sqrt(2)`

C

`+-sqrt(3)`

D

none of these

Text Solution

Verified by Experts

Let m be the slop of the common tanent .Then,
`+-sqrt(3)sqrt(1+m^(2))=+-sqrt(4m^(2)+1)`
or `3+2m^(2)=4m^(2)+1`
or `m^(2)=2`
or `m=+-sqrt(2)`
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