The curve represented by the equation `sqrt(p x)+sqrt(q y)=1` where `p ,q in R ,p ,q >0,` is (a) a circle (b) a parabola (c) an ellipse (d) a hyperbola

The locus of the orthocentre of the triangle formed by the lines (1+p) x-py + p(1 + p) = 0, (1 + q)x-qy + q(1 +q) = 0 and y = 0, where p!=*q , is (A) a hyperbola (B) a parabola (C) an ellipse (D) a straight line

If p + sqrt q = r + sqrts , then

A curve is represented by the equations x=sec^2ta n dy=cott , where t is a parameter. If the tangent at the point P on the curve where t=pi/4 meets the curve again at the point Q , then |P Q| is equal to (5sqrt(3))/2 (b) (5sqrt(5))/2 (c) (2sqrt(5))/3 (d) (3sqrt(5))/2

IF 2+sqrt3i is a root of the equation x^2+px+q=0 where p and q are real, find p and q.

If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal, show that 1/p+1/r=2/q .

If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal ,show that 1/p+1/r=2/q

The normal to a curve at P(x , y) meet the x-axis at Gdot If the distance of G from the origin is twice the abscissa of P , then the curve is a (a) parabola (b) circle (c) hyperbola (d) ellipse

If p + q = sqrt13 p - q = sqrt5 then the value of pq is ____

If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],[ q c ,r a, p b],[ r b, p c, q a]|i s (a) 0 (b) p a+q b+r c (c) 1 (d) none of these

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 p and q .