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The portion of the line x cos alpha+ y s...

The portion of the line `x cos alpha+ y sin alpha= p`, intercepted by the ellipse-`x^2/a^2+y^2/b^2=1` , subtends a right angle at the centre of the ellipse. Prove that the line touches a circle concentric with the ellipse.

Text Solution

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`L1:xcos(alpha)+ ysin(alpha)=p`
Distance of L1 from the center(0,0) is
Distance=`|(p/sqrt((cos(alpha))^2+(sin(alpha)^2)))|=p`
Hence, line touches a circle concentric with ellipse.
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