Basics: Distance, Section Formula, Locus: JEE Questions & Solutions

Among the statements (S1): If A(5,-1) and B(-2,3) are two vertices of a triangle whose orthocentre is (0,0), then its third vertex is…

The number of elements in the relation R={(x,y): 4x²+y²<52, x,y∈ℤ} is

Let the triangle PQR be the image of the triangle with vertices (1, 3), (3, 1) and (2, 4) in the line x + 2y = 2. If the centroid of Δ PQR…

Let ⁿC_(r-1) = 28, ⁿC_r = 56 and ⁿC_(r+1) = 70. Let A (4cos t, 4sin t), B (2sin t, -2cos t) and C (3r - n, r² - n - 1) be the vertices of a…

Let alpha, beta, gamma, delta ∈ ℤ and let A(α, β), B(1, 0), C(γ, δ), and D(1, 2) be the vertices of a parallelogram ABCD. If AB = √10 and…

If the locus of the point, whose distances from the point (2, 1) and (1, 3) are in the ratio 5:4, is ax² + by² + cxy + dx + ey + 170 = 0,…

The equations of the sides AB, BC, and CA of a triangle Δ ABC are: 2x + y = 0, x + py = 21a (a ≠ 0), x - y = 3, and P(2, a) is the centroid…

Let the point (p, p + 1) lie inside the region E = {(x,y): 3 - x ≤ y ≤ √(9 - x²), 0 ≤ x ≤ 3}. If the set of all values of p is the interval…