A curve is given by the equations `x = at^2` &`y=at^3` A variable pair of perpendicular lines throughthe origin 'O' meet the curve at P & Q. Show that the locus of the point of intersection of the tangents at P & Q is `4y^2=3ax-a^2`

A curve is defined parametrically be equations x=t^(2) and y=t^(3) .A variable pair of perpendicular lines through the origin O meet the curve of P and Q. If the locus of the point of intersection of the tangents at P and Q is ay^(2)=bx-1, then the value of (a+b) is

if a variable tangent of the circle x^(2)+y^(2)=1 intersects the ellipse x^(2)+2y^(2)=4 at P and Q. then the locus of the points of intersection of the tangents at P and Q is

Find the locus of the point of intersection of the perpendicular tangents of the curve y^(2)+4y-6x-2=0

A variable chord PQ of the parabola y=4x^(2) subtends a right angle at the vertex. Then the locus of points of intersection of the tangents at P and Q is

The line x+y=1 cuts the coordinate axes at P and Q and a line perpendicular to it meet the axes in R and S. The equation to the locus of the point of intersection of the lines PS and QR is

If the line x-y-1=0 intersect the parabola y^(2)=8x at P and Q, then find the point on intersection of tangents P and Q.

If normal of circle x^(2)+y^(2)+6x+8y+9=0 intersect the parabola y^(2)=4x at P and Q then find the locus of point of intersection of tangent's at P and Q.

Two perpendicular tangents to the circle x^(2)+y^(2)=a^(2) meet at P. Then the locus of P has the equation

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.

Two tangents to the parabola y^(2) = 8x meet the tangent at its vertex in the points P & Q. If PQ = 4 units, prove that the locus of the point of the intersection of the two tangents is y^(2) = 8 (x + 2) .