OPQR is square and M, N are the middle points of the sides PQ and QRrespectively then the ratio of the areas of the square and the triangle OMNis
8 : 3
Taking the coordinate of vertices O,P,Q,R as (0, 0), (a, 0), (a, a), (0, a) respectively we get the coordinates of M as (a, a/2) and of N as (a/2, a)
Area of the square = a2
∴ the required ratio is 8 : 3.
ABCD is a rectangle with A(–1,2),B(3,7) and AB : BC = 4:3. If p isthe center of the rectangle then the distance of p from each corner is equal to
If a (2,0) and (0,2) are given points and p is a point such that PA:PB = 2:3 then the locus of p passes through the point (a,a) for
A(1, 3), B(3, 7) & C(7, 15) are three points. P is the midpoint of AB, Q is the midpoint of BC. Locus of a point R which satisfies (PR)2 – (QR)2 = (AC)2 is
If A(1, a), B(a, a2), C(a2, a2) are the vertices of a triangle which are equidistance from the origin, then the centroid of the triangle ABC is at the point
Given the point A(0, 4) and B(0, –4), the equation of the locus of the pointp(x, y) such that |AP – BP| = 6 is
Coordinate (x, y) of a point P satisfy the relation 3x + 4y = 9, y = mx + 1. The number of integral value of m for which the x-coordinate of p is also an integer is
The point A(2, 3), B(3, 5), C(7, 7) and D(4, 5) are such that
Q, R and S are the points on the line joining the points P(a, x) and T(b, y) such that PQ = QR = RS = ST.
The line joining A(bcos α, bsin α) and B(acos β, asin β) is produced to point M(x, y) so that AM : MB = b : a, then
If p, x1, x2….xi,….and q y1, y2,…yi … are in A.P. with common difference a and b respectively, then locus of the center of mean position of the point Ai (xi, yi), i = 1, 2 …n is