The line `2x - 4y +1 = 0` cuts the circle `x^2 + y^2 = a^2` in two distinct points `P` and `Q`. Equation of the circle having minimum radius that can be drawn through the points P and Q is

The line y=mx+c cuts the circle x^(2)+y^(2)=a^(2) at two distinct points A and B . Equation of the circle having minimum radius that can be drawn through the points A and B is:

If the line y=mx-(m-1) cuts the circle x^(2)+y^(2)=4 at two real and distinct points then

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

The line 4x -7y + 10 = 0 intersects the parabola y^(2) =4x at the points P and Q. The coordinates of the point of intersection of the tangents drawn at the points P and Q are

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 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

A line lx+my+n=0 meets the circle x^(2)+y^(2)=a^(2) at points P and Q. If the tangents drawn at the points P and Q meet at R, then find the coordinates of R.

The equation of the circle having the lines y^(2) – 2y + 4x – 2xy = 0 as its normals & passing through the point (2, 1) is