Home
Class 12
MATHS
Prove that the common tangent of the ell...

Prove that the common tangent of the ellipses `(x^2)/(a^2)+(y^2)/(b^2)-(2x)/c=0 and (x^2)/(b^2)+(y^2)/(a^2)-(2x)/c=0` subtends a right angle at the origin.

Promotional Banner

Similar Questions

Explore conceptually related problems

The number of common tangents to the circles x^(2)+y^(2)-x=0 and x^(2)+y^(2)+x=0 , is

The number of common tangents to the circles x^(2)+y^(2)-x=0 and x^(2)+y^(2)+x=0 are

The number of common tangents to the circles x^(2)+y^(2)-y=0 and x^(2)+y^(2)+y=0 is

The condition that y=m x+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is

If the common chord of the circles x^(2) + ( y -lambda)^(2) =16 and x^(2) +y^(2) =16 subtend a right angle at the origin then ' lambda' is equal to :

If the common chord of the circles x^(2) + ( y -lambda)^(2) =16 and x^(2) +y^(2) =16 subtend a right angle at the origin then ' lambda' is equal to :

The number of common tangents to the circles x^(2)+y^(2)-y=0and x^(2)+y^(2)+y=0 is

If (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b) and x^(2)-y^(2)=c^(2) cut at right angles,then:

(A) Number of values of a for which the common chord of the circles x^(2)+y^(2)=8 and (x-a)^(2)+y^(2)=8 subtends a right angle at the origin is