Point `A(2,1),B(3,-7) , C` is any point on the line `3x-2y = 1` , then locus of point `D` such that `ABCD` is a parallelogram

If P is the point (1,0) and Q is any point on the parabola y^(2) = 8x then the locus of mid - point of PQ is

If P is (3, 1) and Q is a point on the curve y^2 = 8x , then the locus of the mid-point of the line segment PQ is

P is any point in the interior of the parallelogram ABCD. Prove that DeltaAPD+DeltaBPC = 1/2 parallelogram ABCD.

ABCD is a parallelogram. P is any point on AD, such that AP = 1/3AD and Q is a point on BC such that CQ = 1/3BC . Prove that AQCP is a parallelogram.

A B C D is a parallelogram. P is a point on A D such that A P=1/3A D and Q is a point on B C such that C Q=1/3B P . Prove that A Q C P is a parallelogram.

Two circles C_(1) and C_(2) both pass through the points A(1,2) and E(2,1) and touch the line 4x-2y=9 at B and D, respectively. The possible coordinates of a point C, such that the quadrilateral ABCD is a parallelogram,are (a,b). Then the value of |ab| is

Consider the points A(1,2,8), B(0,3,4), C (1,1,3) and D(2,0,7) Prove that ABCD is a parallelogram

If A(-1, 0), B(1, 0) and C(3, 0) are three given points, then the locus of point D satisfying the relation DA^2 + DB^2 = 2DC^2 is (A) a straight line parallel to x-axis (B) a striaght line parallel to y-axis (C) a circle (D) none of these

If A(-1, 0), B(1, 0) and C(3, 0) are three given points, then the locus of point D satisfying the relation DA^2 + DB^2 = 2DC^2 is (A) a straight line parallel to x-axis (B) a striaght line parallel to y-axis (C) a circle (D) none of these