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Analytical Geometry

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6 Feb 2012 10:01:10 IST

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IIT Level- ELLIPSE Question- Includes my try at this question.

Mathematics

The portion of the line , intercepted by the ellipse , subtends a right angle at the centre of the ellipse. Prove that the line touches a circle concentric with the ellipse.

My try-

All I could gather was a condition by homogenising the equation of the ellipse with that of the line and then putting (coeff of x^2) + (coeff of y^2)=0. After that, I am clueless.

Help me out friends.

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HARIKRISHNAN M

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Joined: 30 Aug 2011

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8 Feb 2012 20:50:03 IST

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let the elipse be

x^2/a^2+y^2/b^2=1

and the line be

mx-y=c

homogonize

the coeff x(square)+coeffy(square)=0

you will get the condition

c(square)=sqrt((a(square)b(square)/a(square)+b(square))*sqrt(1+m(square))

which is the condition of line mx-y =c to be a tangent of the cicrcle

c=r*sqrt(1+m(sqauare))

where r is that thing

hope yu understand

Abhinav Sharma

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Joined: 10 Jun 2009

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10 Feb 2012 20:04:47 IST

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I am sorry, the equations did not show up-

Here's the question again-

The portion of the line intercepted by the ellipse , subtends a right angle at the centre of the ellipse. Prove that the line touches a circle concentric with the ellipse.

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