Equation of tangent to parabola `y^2 = 4ax`

Show that the equation of tangent to the parabola y^(2) = 4ax " at " (x_(1), y_(1)) " is " y y_(1)= 2a(x + x_(1))

Find the equation of tangent to the parabola y^(2)=8ax at (2a , 4a)

Find the equation of tangent to the parabola y^(2)=8ax at (2a , 4a)

Equation of normal to parabola y^2 = 4ax at (at^2, 2at) is

Equation of normal to parabola y^2 = 4ax at (at^2, 2at) is

Differential equation of all tangents to the parabola y^2=4ax is (A) y=mx+a/m , m!=0 (B) y_1(yy_1-x)=a (C) xy_1^2-yy_1+a=0 (D) none of these

Show that the equation of the tangent to the parabola y^(2) = 4 ax at (x_(1), y_(1)) is y y_(1) = 2a(x + x_(1)) .

Show that the length of the tangent to the parabola y^2 = 4ax intercepted between its point of contact and the axis of the parabola is bisected by the tangent at the vertex.