Find the directrix of parabola such that from point P tangents are drawn to parabola `y^2= 4ax` having slopes `m_1, m_2` such that `m_1 m_2=-2`

Find the locus of the point P from which tangents are drawn to the parabola y^(2) = 4ax having slopes m_(1) and m_(2) such that m_(1)^(2)+m^(2)=lamda (constant) where theta_(1) and theta_(2) are the inclinations of the tangents from positive x-axis.

Find the locus of the point P from which tangents are drawn to the parabola y^(2) = 4ax having slopes m_(1) and m_(2) such that theta_(1)-theta_(2)=theta_(0) (constant) where theta_(1) and theta_(2) are the inclinations of the tangents from positive x-axis.

Equation of normal to the parabola y^(2)=4ax having slope m is

If from a point A, two tangents are drawn to parabola y^2 = 4ax are normal to parabola x^2 = 4by , then

If from a point A,two tangents are drawn to parabola y^(2)=4ax are normal to parabola x^(2)=4by, then

From a point P, two tangents are drawn to the parabola y^(2) = 4ax . If the slope of one tagents is twice the slope of other, the locus of P is

From a point P, two tangents are drawn to the parabola y^(2) = 4ax . If the slope of one tagents is twice the slope of other, the locus of P is

Find the slope of the tangent to the parabola y^2=4ax at (at^2,2at) .

If the line px + qy =1m is a tangent to the parabola y^(2) =4ax, then