If the line 2x+5y=12 intersects the ellipse `4x^(2)+5y^(2)=20` in two distinct points A and B ,then the midpoint of AB is

The line 3x+5y=k touches the ellipse 16x^(2)+25y^(2)=400 ,if k is

The line x+2y=1 cuts the ellipse x^(2)+4y^(2)=1 1 at two distinct points A and B. Point C is on the ellipse such that area of triangle ABC is maximum, then find point C.

A tangent to the hyperbola x^(2)/4 - y^(2)/1 = 1 meets ellipse x^(2) + 4y^(2) = 4 in two distinct points . Then the locus of midpoint of this chord is

The line x+2y=a intersects the circle x^(2)+y^(2)=4 at two distinct points A and B Another line 12x-6y-41=0 intersects the circle x^(2)+y^(2)-4x-2y+1=0 at two C and D. The value of a' for which the points A,B,C and D are concyclic-

The line 2x+y=3 intersects the ellipse 4x^(2)+y^(2)=5 at two points. The point of intersection of the tangents to the ellipse at these point is

The line x+2y+a=0 intersects the circle x^2+y^2-4=0 at two distinct points A and B. Another line 12x-6y-41=0 intersects the circle x^2+y^2-4x-2y+1=0 at two distincts points C and D. The value of 'a' so that the line x+2y+a=0 intersects the circle x^2+y^2-4=0 at two distinct points A and B is

If the line y=3x+lambda intersects the parabola y^(2)=4x at two distinct points then set of values of lambda

The circle with equation x^(2)+y^(2)=1 intersects the line y=7x+5 at two distinct points A and B. Let C be the point at which the points A and B.Let C be the point at which the positive x-axis intersects the circle.The angle ACB is