`y=x+1` intersect the ellipse `x^2/4+y^2/2=1` at the point P and Q. PQ is the diameter of the circle then the value of `(3r)^2`

The line x=2y intersects the ellipse (x^(2))/4+y^(2)=1 at the points P and Q . The equation of the circle with PQ as diameter is

A variable tangent to the circle x^(2)+y^(2)=1 intersects the ellipse (x^(2))/(4)+(y^(2))/(2)=1 at point P and Q. The lous of the point of the intersection of tangents to the ellipse at P and Q is another ellipse. Then find its eccentricity.

A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C_1 : x^2 + y^2 + 2y -5 = 0 at two points P and Q such that PQ is a diameter of C^1 . Then the diameter of C is :

Lines x+y=1 and 3y=x+3 intersect the ellipse x^(2)+9y^(2)=9 at the points P,Q,R. the area of the triangles PQR is

The straight line (x)/(4)+(y)/(3)=1 intersects the ellipse (x^(2))/(16)+(y^(2))/(9)=1 at two points A and B there is a point P on this ellipse such that the area of Delta PAB is equal to 6(sqrt(2)-1) . Then the number of such point (P) is/are (A) 4 (B) 1 (C) 2 (D) 3

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

If the straight line x-2y+1=0 intersects the circle x^(2)+y^(2)=25 at points P and Q, then find the coordinates of the point of intersection of the tangents drawn at P and Q to the circle x^(2)+y^(2)=25

if a variable tangent of the circle x^(2)+y^(2)=1 intersects the ellipse x^(2)+2y^(2)=4 at P and Q. then the locus of the points of intersection of the tangents at P and Q is

A line y=2x+c intersects the circle x^(2)+y^(2)-2x-4y+1=0 at P and Q. If the tangents at P and Q to the circle intersect at a right angle,then |c| is equal to