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

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 x+y=a touches the parabola y=x-x^2, then find the value of a .

Find the equation of the tangent to the parabola y^(2)=8x at the point (2t^(2),4t) . Hence find the equation of the tangnet to this parabola, perpendicular to x+2y+7=0

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

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 line x+y =1 is a tangent to the parabola y^(2)-y +x=0 , then the point of contact is-

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.

If (2,-8) is at an end of a focal chord of the parabola y^2=32 x , then find the other end of the chord.

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 find Q_(2)Q_(3)=12 and R_(2)R_(3)=4sqrt(6)