If the line `y=3x+c` touches the parabola `y^2=12 x` at point `P` , then find the equation of the tangent at point `Q` where `P Q` is a focal chord.

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 the normal at P(18, 12) to the parabola y^(2)=8x cuts it again at Q, then the equation of the normal at point Q on the parabola y^(2)=8x is

The line 4x -7y + 10 = 0 intersects the parabola y^(2) =4x at the points P and Q. The coordinates of the point of intersection of the tangents drawn at the points P and Q are

Consider the parabola y^(2)=8x, if the normal at a point P on the parabola meets it again at a point Q, then the least distance of Q from the tangent at the vertex of the parabola is

Consider the parabola y^(2)=8x, if the normal at a point P on the parabola meets it again at a point Q, then the least distance of Q from the tangent at the vertex of the parabola is

The circle C1 : x^2 + y^2 = 3 , with center at O, intersects the parabola x^2 = 2y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2 and C3 at R2 and R3, respectively. Suppose C2 and C3 have equal radii 2sqrt(3) and centers Q2 and Q3, respectively.If Q_2 and Q_3 lies on the y-axis, then

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

If the angle between the normal to the parabola y^(2)=4ax at point P and the focal chord passing through P is 60^(@) , then find the slope of the tangent at point P.

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 .

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 .