l f y+b= `m_(1)`(x+ a) and y+b=`m_(2)` (x+a) are two tangents to `y^(2) = 4ax`, then show that `m_(1)m_(2) = -1. `

If (x_(1),y_(1)) and (x_(2),y_(2)) are the ends of a focal chord of the parabola y^(2) = 4ax then show that x_(1),x_(2)=a^(2),y_(1),y_(2)= -4a^(2)

If (x_(1),y_(1)) and (x_(2),y_(2)) are ends of focal chord of y^(2)=4ax then x_(1)x_(2)+y_(1)y_(2) =

Assertion (A) : the sum and product of the slopes of the tangents to the ellipse (x^2)/(9)+(y^2)/(4)=1 drawn from the points (6,-2) are -8/9 ,1. Reason(R): if m_(1),m_(2) are the slopes of the tangents through (x_(1),y_(1)) of the ellipse, then m_(1)+m_(2)=(2x_(1).y_(1))/(x_(1)^(2)-a^(2)) m_(1).m_(2)=(y_(1)^(2)-b^(2))/(x_(1)^(2)-a^(2))

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) .

The line y =m(x+a) + a/m touch the parabola y^(2)=4a(x+a) for m

If y = 2x is tangent to the curve y^2 = ax^3 + b at (1, 2) , then (a, b) =

If the normals at (x_(1),y_(1)) and (x_(2) ,y_(2)) on y^(2) = 4ax meet again on parabola then x_(1)x_(2)+y_(1)y_(2)=