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.

Point of intersection of tangents at P(alpha) and Q(Beta)

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

If the eccentric angles of two points P and Q on the ellipse x^2/a^2+y^2/b^2 are alpha,beta such that alpha +beta=pi/2 , then the locus of the point of intersection of the normals at P and Q is

If two normals drawn from any point to the parabola y^(2) = 4ax make angle alpha and beta with the axis such that tan alpha . tan beta = 2, then find the locus of this point,

Find the equation of a plane which meets the axes in A,B and C, given that the centroid of the triangle ABC is the point (alpha,beta,gamma)

Tangents are drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at two points whose eccentric angles are alpha-beta and alpha+beta The coordinates of their point of intersection are

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

I If a point (alpha,beta) lies on the circle x^(2)+y^(2)=1 then the locus of the point (3 alpha.+2,beta), is