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Length of the perpendicualar from the ce...

Length of the perpendicualar from the centre of the ellipse `27x^(2)+9y^(2)=243` on a tangent drawn to it which makes equqal intercepts on the coordiantes axes is

A

`3//2`

B

`3sqrt(2)`

C

`3//sqrt(3)`

D

6

Text Solution

Verified by Experts

The correct Answer is:
B
Given ellipse is `(x^(2))/(9)+(y^(2))/(37)=1`
Tangent to ellipse having slop m is y = `mx+-sqrt(a^(2)m^(2)+b^(2))`
Since tangent makes equal intercepts on the coordinates axes, m=-1
`y=-x+-6`
or `x+y+6=0`
`:.` Length of perpendicular from (0,0)`|(6)/(sqrt(2))|=3sqrt(2)`
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