If the normals to the parabola `y^2=4a x` at three points `(a p^2,2a p),` and `(a q^2,2a q)` are concurrent, then the common root of equations `P x^2+q x+r=0` and `a(b-c)x^2+b(c-a)x+c(a-b)=0` is `p` (b) `q` (c) `r` (d) `1`

The chord of contact of tangents from three points P, Q, R to the circle x^(2) + y^(2) = c^(2) are concurrent, then P, Q, R

If p and q are the roots of the equation x^2-p x+q=0 , then p=1,\ q=-2 (b) b=0,\ q=1 (c) p=-2,\ q=0 (d) p=-2,\ q=1

Prove that equations (q-r)x^(2)+(r-p)x+p-q=0 and (r-p)x^(2)+(p-q)x+q-r=0 have a common root.

If sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-2) (b) p^2=q(q+2) (c)p^2q^2=2q (d) none of these

If p and q are the roots of the equation x^2 - 15x + r = 0 and. p - q = 1 , then what is the value of r?

The value of p and q(p!=0,q!=0) for which p,q are the roots of the equation x^(2)+px+q=0 are (a)p=1,q=-2(b)p=-1,q=-2(c)p=-1,q=2(d)p=1,q=2

P, Q, and R are the feet of the normals drawn to a parabola ( y−3 ) ^2 =8( x−2 ) . A circle cuts the above parabola at points P, Q, R, and S . Then this circle always passes through the point. (a) ( 2, 3 ) (b) ( 3, 2 ) (c) ( 0, 3 ) (d) ( 2, 0 )

If the ratio of the roots of the equation x^(2)+px+q=0 are equal to ratio of the roots of the equation x^(2)+bx+c=0, then prove that p^(2c)=b^(2)q

The normals at three points P,Q,R of the parabola y^(2)=4ax meet in (h,k) The centroid of triangle PQR lies on (A)x=0(B)y=0(C)x=a(D)y=a^(*)