Prove that the tangent to the parabola `y^2=4ax` at `(a/(m^2),(2a)/m)` is `y=m x+a/m.`

Prove that the tangent to the parabola y^(2)=4ax at ((a)/(m^(2)),(2a)/(m)) is y=mx+(a)/(m)

A : The sum and product of the slopes of the tangents to the parabola y^(2)=8x drawn form the point (-2,3) are -3/2,-1 . R : If m_(1),m_(2) are the slopes of the tangents of the parabola y^(2) =4ax through P (x_(1),y_(1)) then m_(1)+m_(2)=y_(1)//x_(1),m_(1)m_(2)=a//x_(1) .

If y+b=m_1(x+a)& y+b=m_2(x+a) are two tangents to the parabola y^2=4ax then |m_1m_2| is equal to:

The line y=m x+2 is a tangent to the parabola y^(2)=4 x, then m=

Show that the condition that the line y=mx+c may be a tangent to the parabola y^(2)=4ax is c=(a)/(m)

If the line y=m x+c is a tangent to the parabola y^(2)=4 a(x+a) , then c=

The line y=mx+1 is tangent to the parabola y^2=4x if m is _____.

Let the tangents to the parabola y^(2)=4ax drawn from point P have slope m_(1) and m_(2) . If m_(1)m_(2)=2 , then the locus of point P is

Let the tangents to the parabola y^(2)=4ax drawn from point P have slope m_(1) and m_(2) . If m_(1)m_(2)=2 , then the locus of point P is