At any point P on the parabola `y^2 -2y-4x+5=0` a tangent is drawn which meets the directrix at Q. Find the locus of point R which divides QP externally in the ratio `1/2:1`

If Q is a point on the locus of x^(2)+y^(2)+4x-3y+7=0 , then find the equation of locus of P which divides segment OQ externally in the ratio 3:4, where O is origin.

If Q is a point on the locus of x^(2) + y^(2) + 4x - 3y +7=0 , then find the equation of locus of P which divides segment OQ externally in the ratio 3:4, where O is the origin.

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

Normals are drawn at points A, B, and C on the parabola y^2 = 4x which intersect at P. The locus of the point P if the slope of the line joining the feet of two of them is 2, is

Let N be the foot of perpendicular to the x-axis from point P on the parabola y^2=4a xdot A straight line is drawn parallel to the axis which bisects P N and cuts the curve at Q ; if N Q meets the tangent at the vertex at a point then prove that A T=2/3P Ndot

Normal to the ellipse (x^2)/(64)+(y^2)/(49)=1 intersects the major and minor axes at Pa n dQ , respectively. Find the locus of the point dividing segment P Q in the ratio 2:1.

From any point P on the parabola y^(2)=4ax , perpebdicular PN is drawn on the meeting it at N. Normal at P meets the axis in G. For what value/values of t, the point N divides SG internally in the ratio 1 : 3, where S is the focus ?

Tangents are drawn to the parabola y^2=4a x at the point where the line l x+m y+n=0 meets this parabola. Find the point of intersection of these tangents.

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Qa n dR , then find the midpoint of chord Q Rdot