Prove that if any tangent to the ellipse is cut by the tangents at the endpoints of the major axis at `Ta n dT '` , then the circle whose diameter is `T T '` will pass through the foci of the ellipse.

A tangent to the ellipse 4x^2 +9y^2 =36 is cut by the tangent at the extremities of the major axis at T and T^1 , the circle on T T^1 as diameter passes through the point

The tangent at any point on the ellipse 16x^(2)+25y^(2) = 400 meets the tangents at the ends of the major axis at T_(1) and T_(2) . The circle on T_(1)T_(2) as diameter passes through

y-axis is a tangent to one ellipse with foci (2,0) and (6,4) if the length of the major axis is then [x]=_____

The equation of tangent to the ellipse 2x^(2)+3y^(2)=6 which make an angle 30^(@) with the major axis is

The tangents and normal at a point on (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 cut the y-axis A and B. Then the circle on AB as diameter passes through the focii of the hyperbola

Find the equation of the tangents drawn at the ends of the major axis of the ellipse 9x^(2)+5y^(2)-30y=0

The tangent at a point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 , which in not an extremely of major axis meets a directrix at T. Statement-1: The circle on PT as diameter passes through the focus of the ellipse corresponding to the directrix on which T lies. Statement-2: Pt substends is a right angle at the focus of the ellipse corresponding to the directrix on which T lies.

Prove that the tangent at any point of circle is perpendicular to the radius through the point of contact.

Prove that the tangent at any point of circle is perpendicular to the radius through the point of contact.

If a circle is concentric with the ellipse, find the in­clination of their common tangent to the major axis of the ellipse.