If the abscissa and ordinates of two points `Pa n dQ` are the roots of the equations `x^2+2a x-b^2=0` and `x^2+2p x-q^2=0` , respectively, then find the equation of the circle with `P Q` as diameter.

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

The abscissa and ordinates of the endpoints Aa n dB of a focal chord of the parabola y^2=4x are, respectively, the roots of equations x^2-3x+a=0 and y^2+6y+b=0 . Then find the equation of the circle with A B as diameter.

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

If the roots of the quadratic equation x^(2)+px+q=0 are tan 30^(@)" and "tan15^(@) , respectively then the value of 2+q-p is

Show that , if p,q,r are rational , the roots of the equation x^2-2px+p^2-q^2+2pr-r^2=0 are rational .

If the equation p x^2+(2-q)x y+3y^2-6q x+30 y+6q=0 represents a circle, then find the values of pa n dqdot

If -4 is a root of the equation x^(2)+px-4=0 and if the equation x^(2)+px+q=0 are equal roots, find the values of p and q.

Find the parametric form of the equation of the circle x^2+y^2+p x+p y=0.

If the roots of the equation q^2 x^2 + p^2 x + r^2 =0 are the squares of the roots of the equation qx^2 + px + r=0 , then p,q,r are in ………………….. .