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 the line y-sqrt(3)x+3=0 cut the parabola y^2=x+2 at P and Q , then A PdotA Q is equal to

The focal chord of the parabola y^2=a x is 2x-y-8=0 . Then find the equation of the directrix.

Find the equation of the tangent to the parabola y=x^2-2x+3 at point (2, 3).

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 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 .

The circle C_(1):x^(2)+y^(2)=3 , with centre at O, intersects the parabola x^(2)=2y at the point P in the quadrant. Let the tangent to the circle C_(1) at P touches other tqo circles C_(2)andC_(3) at R_(2)andR_(3) , respectively. Suppose C_(2)andC_(3) have equal radii 2sqrt(3) and centres Q_(2)andQ_(3) . respectively. If Q_(2)andQ_(3) lie on the y-axis, then

If PQ is the focal chord of parabola y=x^(2)-2x+3 such that P-=(2,3) , then find slope of tangent at Q.

Find the equation of tangents of the parabola y^2=12 x , which passes through the point (2, 5).