A circle with center at the origin and radius equal to a meets the axis of `x` at `Aa n dBdotP(alpha)` and `Q(beta)` are two points on the circle so that `alpha-beta=2y` , where `gamma` is a constant. Find the locus of the point of intersection of `A P` and `B Qdot`

A circle x^(2)+y^(2)=a^(2) meets the x-axis at A(-a,0) and B(a,0). P(alpha) and Q( beta ) are two points on the circle so that alpha-beta=2 gamma, where gamma is a constant. Find the locus of the point of intersection of AP and BQ.

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

Two variable chords A Ba n dB C of a circle x^2+y^2=r^2 are such that A B=B C=r . Find the locus of the point of intersection of tangents at Aa n dCdot

The coordinates of the point Aa n dB are (a,0) and (-a ,0), respectively. If a point P moves so that P A^2-P B^2=2k^2, when k is constant, then find the equation to the locus of the point Pdot

If the tangents are drawn to the circle x^2+y^2=12 at the point where it meets the circle x^2+y^2-5x+3y-2=0, then find the point of intersection of these tangents.

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot

Two variable chords AB and BC of a circle x^(2)+y^(2)=a^(2) are such that AB=BC=a . M and N are the midpoints of AB and BC, respectively, such that the line joining MN intersects the circles at P and Q, where P is closer to AB and O is the center of the circle. The locus of the points of intersection of tangents at A and C is

If P is any point on the plane l x+m y+n z=pa n dQ is a point on the line O P such that O PdotO Q=p^2 , then find the locus of the point Qdot

If P is any point on the plane l x+m y+n z=pa n dQ is a point on the line O P such that O PdotO Q=p^2 , then find the locus of the point Qdot

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