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 (a)`p` (b) `q` (c) `r` (d) `1`

If p and q are the roots of the equation x^(2)+px+q=0 , then

If a ,b ,p ,q are nonzero real numbers, then how many comman roots would two equations 2a^2x^2-2a b x+b^2=0a n dp^2x^2+2p q x+q^2=0 have?

Normals of parabola y^2=4 x at P and Q meet at R(x_2, 0) and tangents at P and Q mect-at T(x_1, 0) . If x_2=3 , then find the area of quadrilateral P T Q R .

A normal drawn to the parabola y^2=4a x meets the curve again at Q such that the angle subtended by P Q at the vertex is 90^0dot Then the coordinates of P can be (a) (8a ,4sqrt(2)a) (b) (8a ,4a) (c) (2a ,-2sqrt(2)a) (d) (2a ,2sqrt(2)a)

If one root is square of the other root of the equation x^2+p x+q=0 then the relation between p and q is

If the roots of the equation (q-r)x^(2)+(r-p)x+p-q=0 are equal, then show that p, q and r are in A.P.

The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are