Help with a parametrics question!?

Question

The chord of contact of two tangents drawn from an external point P to the parabola x^2=8y has equation x + 2y - 3 = 0. Find the coordinates of P. 
 

 

 

Answer 1

The parabola is   and the  chord of contact is x + 2 y - 3 = 0.

From the equation of chord of contact,   ....................( 1 )

Rewriting the equation x + 2y - 3 = 0 that is 2y +x -3 =0

     ..................( 2 )

Comparing equations (1) and (2),

  and  

The equation of parabola in parametric form is  .

 

       = 

So the value of  a = 2 .

The point of intersection of tangents is  ( a(p+q),apq ).

a ( p + q ) = 2( -1)  = - 2  and .

So, the  coordinates of P are ( -2 , -3/2 ).