The tangent at any point P on the circle `x^(2)+y^(2)=2`, cuts the axes at L and M. Find the equation of the locus of the midpoint L.M.

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at A and B . Then find the locus of the midpoint of A Bdot

The tangent at any point on the curve x=acos^3theta,y=asin^3theta meets the axes in Pa n dQ . Prove that the locus of the midpoint of P Q is a circle.

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

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

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

If px+qy=r be a tangent to the circle x^(2)+y^(2)=a^(2) at any given point then find the equatin of the normal to the circle at the same point.

If the tangent at any point of the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) meets the coordinate axes in A and B, then show that the locus of mid-points of AB is a circle.

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 centre is

The straight line 3x-4y +7 = 0 is a tangent to the circle x^(2) + y^(2) + 4x + 2y + 4 = 0 at P, find the equation of its normal at the same point.

A variable plane which is at a constant distance 3p from the origin O cuts the axes at L,M and N.Show that the locus of the points of intersection of the planes through L,M,N drwon parallel to the coordinate planes is 9(x^(-2)+y^(-2)+z^(-2))=p^(-2) .