Find the point where the line `x+y=6` is a normal to the parabola `y^2=8xdot`

Prove that the chord y-xsqrt(2)+4asqrt(2)=0 is a normal chord of the parabola y^2=4a x . Also find the point on the parabola when the given chord is normal to the parabola.

Find the equations of the tangent and normal to the parabola y^(2)=8x at t=1/2

Find the equations of the tangent and normal to the parabola y^(2) = 4ax at the point (at^(2) , 2at).

If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b), then the value of a+b is ___________ .

Find the equation of line which is normal to the parabola x^(2)=4y and touches the parabola y^(2)=12x .

Find the angle between the tangents drawn from (1, 3) to the parabola y^2=4xdot

Tangents are drawn to the parabola y^2=4a x at the point where the line l x+m y+n=0 meets this parabola. Find the point of intersection of these tangents.

Find the shortest distance between the line y=x-2 and the parabola y=x^2+3x+2.

Find the shortest distance between the line y=x-2 and the parabola y=x^2+3x+2.

From the point (4,6) , a pair of tangent lines is drawn to the parabola y^2=8 x . The area of the triangle formed by these pairs of tangent lines and the chord of contact of the point (4,6) is