sides are parallel to the coordinate axes. Another ellipse E passing through the point( , ) circumscribes the rectangle R . The eccentricity of the ellipse is ( ) ( ) ( ) ( ) . Tangents are drawn to the hyperbola x = parallel to the straight line = .
One of the points of contact of tangents on the hyperbola is ( ) , − ( ) ( ) ( ) , − . The equation of the circle passing through the foci of the ellipse x = having centre at ( , ) is ( ) x ( ) x ( ) x ( ) x - - Two Dimensional Analytical Geometry - II . Let C be the circle with centre at( , ) and radius = . If T is the circle centered at( , ) y passing through the origin and touching the circle C externally, then the radius of T is equal to ( ) ( ) ( ) ( ) .
Consider an ellipse whose centre is of the origin and its major axis is along x -axis. If its eccentrcity is and the distance between its foci is , then the area of the quadrilateral inscribed in the ellipse with diagonals as major and minor axis of the ellipse is ( ) ( ) ( ) ( ) . Area of the greatest rectangle inscribed in the ellipse x = is ( ) ab ( ) ab ( ) ab ( ) a . An ellipse has OB as semi minor axes, F and ′ F its foci and the angle FBF ′ is a right angle.
Then the eccentricity of the ellipse is ( ) ( ) ( ) ( ) . The eccentricity of the ellipse ( is ( ) ( ) ( ) ( ) . If the two tangents drawn from a point P to the parabola y are at right angles then the locus of P is ( ) x + = ( ) x