The locus of the orthocenter of the triangle formed by the line (1+p)x-py+p(1+p) = 0, (1+q)x-qy+q(1+q) = 0 and y =0, whete `p ne q,` is

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

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

Statement-l: If the diagonals of the quadrilateral formed by the lines px+ gy+ r= 0, p'x +gy +r'= 0, p'x +q'y +r'= 0 , are at right angles, then p^2 +q^2= p^2+q^2 . Statement-2: Diagonals of a rhombus are bisected and perpendicular to each other.

Show that the reflection of the line px+qy+r=0 in the line x+y+1 =0 is the line qx+py+(p+q-r)=0, where p!= -q .

The equations of the tangents drawn from the origin to the circle x^2 + y^2 - 2px - 2qy + q^2 = 0 are perpendicular if (A) p^2 = q^2 (B) p^2 = q^2 =1 (C) p = q/2 (D) q= p/2

The point of injtersection of the line x/p+y/q=1 and x/q+y/p=1 lies on the line

Point P lie on hyperbola 2xy=1 . A triangle is contructed by P, S and S' (where S and S' are foci). The locus of ex-centre opposite S (S and P lie in first quandrant) is (x+py)^(2)=(sqrt(2)-1)^(2)(x-y)^(2)+q , then the value of p+q is

The value of 1.999 ….. In the form of p/q , where p and q are integers and q ne 0 , is

The vertices of a triangle are (p q ,1/(p q)),(p q)),(q r ,1/(q r)), and (r q ,1/(r p)), where p ,q and r are the roots of the equation y^3-3y^2+6y+1=0 . The coordinates of its centroid are (1,2) (b) (2,-1) (c) (1,-1) (d) (2,3)

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