A line is drawn through a fix point P(`alpha, beta`) to cut the circle `x^2 + y^2 = r^2` at A and B. Then PA.PB is equal to :

If a line passes through the point P(1,-2) and cuts the x^2+y^2-x-y= 0 at A and B , then the maximum of PA+PB is

In the figure ,PA and PB are tangents to the circle drawn from an external point P. also CD is a tangent to the circle at Q. if PA = 8 cm and CQ = 3cm , then PC is equal to …………..

If a circle passes through the point (a, b) and cuts the circle x^2 +y^2=k^2 orthogonally, then the equation of the locus of its center is

Through a fixed point (h, k) secants are drawn to the circle x^2 +y^2 = r^2 . Then the locus of the mid-points of the secants by the circle is

If a circle Passes through a point (1,2) and cut the circle x^2+y^2 = 4 orthogonally,Then the locus of its centre is

If two tangents drawn from the point (alpha,beta) to the parabola y^2=4x are such that the slope of one tangent is double of the other, then prove that alpha=2/9beta^2dot

A circle touching the line x +y - 2 = 0 at (1,1) and cuts the circle x^(2) +y^(2) +4x +5y - 6 = 0 at P and Q. Then

The angle between the pair of tangents drawn from a point P to the circle x^2+y^2+4x-6y+9sin^2alpha+13cos^2alpha=0 is 2alpha . then the equation of the locus of the point P is

Tangent drawn from the point P(4,0) to the circle x^2+y^2=8 touches it at the point A in the first quadrant. Find the coordinates of another point B on the circle such that A B=4 .

The circle x^2 + y^2 - 3x - 4y + 2 = 0 cuts the x axis at the points