A variable line through the point `(p, q)` cuts the `x and y` axes at `A and B` respectively. The lines through `A and B` parallel to y-axis and x-axis respectively meet at `P`. If the locus of `P` is `3x+2y-xy=0`, then (A) `p=2, q=3` (B) `p=3, q=2` (C) `p=2, q=-3` (D) `p=-3, q=-2`

A line intersects the Y- axis and X-axis at the points P and Q, respectively. If (2,-5) is the mid- point of PQ, then the coordinates of P and Q are, respectively.

The line through P(5, 3) intersects y-axis at Q. Find the co-ordinates of Q.

The line segment joining the points (3,\ -4) and (1,\ 2) is trisected at the points P and Q . If the coordinates of P and Q are (p ,\ -2) and (5//3,\ q) respectively. Find the values of p and q .

A straight line L through the origin meets the lines x + y = 1 and x + y = 3 at P and Q respectively. Through P and Q two straight lines L_1 , and L_2 are drawn, parallel to 2x-y- 5 and 3x +y 5 respectively. Lines L_1 and L_2 intersect at R. Locus of R, as L varies, is

A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, 5) is the mid-point of PQ, then find the coordinates of P and Q.

T P and T Q are tangents to the parabola y^2=4a x at P and Q , respectively. If the chord P Q passes through the fixed point (-a ,b), then find the locus of Tdot

P and Q have co-ordinates (-2, 3) and (5, 4) respectively. Reflect P in the x-axis to P' and Q in the y-axis to Q'. State the co-ordinates of P' and 'Q .

The parabola y=x^2+p x+q cuts the straight line y=2x-3 at a point with abscissa 1. Then the value of pa n dq for which the distance between the vertex of the parabola and the x-axis is the minimum is (a) p=-1,q=-1 (b) p=-2,q=0 (c) p=0,q=-2 (d) p=3/2,q=-1/2

The line L_1-=4x+3y-12=0 intersects the x-and y-axies at A and B , respectively. A variable line perpendicular to L_1 intersects the x- and the y-axis at P and Q , respectively. Then the locus of the circumcenter of triangle A B Q is (a) 3x-4y+2=0 (b) 4x+3y+7=0 (c) 6x-8y+7=0 (d) none of these

In the quadratic equation x^2+(p+i q)x+3i=0,p&q are real. If the sum of the squares of the roots is 8 then: p=3,q=-1 b. p=3,q=1 c. p=-3,q=-1 d. p=-3,q=1