Tangent is drawn at any point(p,q) on the parabola y^2=4*a*x,

Tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2, such that all the chords of contact pass through a fixed point ( r,s) then

p,q,r,and s satisfy

A)     (r^2) * q=4 * p^2 * s

B)     rq^2 = 4*p*s^2

C)     r*q^2 = -4* p*s^2

D)     a^2 = -p*r

plz. solve or give a clue to eliminate options , this a multi choice so more than one answer may be correct   

. rates assured

Let us choose (p,q) as parametric point   (p,q) = ( at^2 , 2at)  

i.e   p = at^2    q = 2at

Now eqution of tangent through this line will be

y = x/t + at 

So any point on this tangent can be taken as     (  h ,  h/t + at )

Any outside point (h,k) will have two tangents to a circle...and one chord of contact ....

Cricle is  x^2 + y^2 = a^2   ...if (h,k) is the point chord of contact will have equation...

hx +  ky = a^2 ...

Here we have   ( h , h/t + at )    as outside point == (h,k)

Hence equation of chord of contact is     hx + y( h/t + at ) = a^2

(hx  - yh/t ) + (yat - a^2) = 0

h( x - y/t )  +  a ( yt - a ) = 0

(x-yt) + a/h ( yt-a) = 0 

x = yt      and   yt = a =>  y = a/t

so   x = a

hence the fixed point is   ( a, a/t ) =  ( r,s )

So  r = a       s = a/t         p = at^2    q = 2at

A)     (r^2) * q=4 * p^2 * s 

B)     rq^2 = 4*p*s^2 ;

C)     r*q^2 = -4* p*s^2

D)     a^2 = -p*r

Now put and check the option