If `y=x+2` is normal to the parabola `y^2=4a x ,` then find the value of `a`.

If the line y=m x+1 is tangent to the parabola y^2=4x , then find the value of m .

If the line y=m x+1 is tangent to the parabola y^2=4x , then find the value of mdot

From a point (sintheta,costheta) , if three normals can be drawn to the parabola y^(2)=4ax then find the value of a .

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 ___________ .

If (-2a,a+1) lies in the interior (smaller region) bounded by the circle x^2+y^2=4 and the parabola y^2=4ax , then find the values of a

If y=2x+3 is a tangent to the parabola y^2=24 x , then find its distance from the parallel normal.

If y=2x+3 is a tangent to the parabola y^2=24 x , then find its distance from the parallel normal.

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

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

Statement 1: The line a x+b y+c=0 is a normal to the parabola y^2=4a xdot Then the equation of the tangent at the foot of this normal is y=(b/a)x+((a^2)/b)dot Statement 2: The equation of normal at any point P(a t^2,2a t) to the parabola y^2 = 4a x is y=-t x+2a t+a t^3