The normals at P,Q and R are concurrent and PQ meets the diameter through R on the directrix x=-a . Prove that PQ touches [or PQ enveleopes] the parabola `y^2+16a(x+a)=0`.

The normals at P, Q, R on the parabola y^2 = 4ax meet in a point on the line y = c. Prove that the sides of the triangle PQR touch the parabola x^2 = 2cy.

PQ is a double ordinate of the ellipse x^2+9y^2 =9 , the normal at P meets the diameter through Q at R .then the locus of the mid point of PR is

The normal at P(8, 8) to the parabola y^(2) = 8x cuts it again at Q then PQ =

The normals at the extremities of a chord PQ of the parabola y^2 = 4ax meet on the parabola, then locus of the middle point of PQ is

PQ is a double ordinate of the parabola y^2 = 4ax . If the normal at P intersect the line passing through Q and parallel to axis of x at G, then locus of G is a parabola with -

The straight line 2x+3y =24 meets the x-axis at P and the y-axis at Q. The perpendicular bisector of PQ meets the line through (-2,0) parallel to the y-axis at R. Find the area of the DeltaPQR .

The normal to the parabola y^(2)=4x at P (1, 2) meets the parabola again in Q, then coordinates of Q are

The normal to the parabola y^(2)=4x at P(9, 6) meets the parabola again at Q. If the tangent at Q meets the directrix at R, then the slope of another tangent drawn from point R to this parabola is

If a chord PQ of the parabola y^2 = 4ax subtends a right angle at the vertex, show that the locus of the point of intersection of the normals at P and Q is y^2 = 16a(x - 6a) .

The given figure shows PQ = PR and angle Q = angle R . Prove that Delta PQS = Delta PRT