Any ordinate MP of an ellipse meets the auxillary circle in Q. Ptove that the locus of the point of intersection of the normals at P and Q is the circle `x^(2)+y^(2)=(a+b)^(2)`.

Any ordinate MP of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 meets the auxiliary circle at Q. Then locus of the point of intersection of normals at P and Q to the respective curves at x^(2)+y^(2)=8( b) x^(2)+y^(2)=34x^(2)+y^(2)=64 (d) x^(2)+y^(2)=15

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

The ordinates of points P and Q on the parabola y^2=12x are in the ration 1:2 . Find the locus of the point of intersection of the normals to the parabola at P and Q.

the locus of the point of intersection of tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which meet at right , is

A variable chord PQ of the parabola y^(2) = 4x is drawn parallel to the line y = x. If the parameters of the points P & Q on the parabola are p & q respectively, show that p + q = 2. Also show that the locus of the point of intersection of the normals at P & Q is 2x - y = 12.

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 line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

The tangents PA and PB are drawn from any point P of the circle x^(2)+y^(2)=2a^(2) to the circle x^(2)+y^(2)=a^(2) . The chord of contact AB on extending meets again the first circle at the points A' and B'. The locus of the point of intersection of tangents at A' and B' may be given as

P is a point on the ellipse x^2/(25)+y^2/(9) and Q is corresponding point of P on its auxiliary circle. Then the locus of point of intersection of normals at P" & "Q to the respective curves is