Let `P(x_1, y_1) and Q(x_2, y_2), y_1 < 0, y_2 < 0`, be the end points of the latus rectum of the ellipse `x^2+4y^2 = 4`. The equations of parabolas with latus rectum PQ are

Find the distance between points P(x_1, y_1) and Q(x_2, y_2) : PQ is parallel to y-axis

Find the distance between points P(x_1, y_1) and Q(x_2, y_2) : PQ is parallel to x-axis

Let PQ be a line segment with P(x_1, y_1, z_1) and Q(x_2, y_2, z_2) and let L. be a straight line whose d.c.'s are l, m, n. Then the length of projection of PQ on the line L is

The ratio in which the line segment joining P(x_1, y_1) and Q(x_2, y_2) is divided by x-axis is y_1: y_2 (b) y_1: y_2 (c) x_1: x_2 (d) x_1: x_2

For points P = (x_1, y_1) and Q = (x_2,y_2) of the coordinate plane, a new distance d (P, Q) is defined by d(P,Q)=|x_1-x_2|+|y_1-y_2|. Let O (0, 0) and A = (3, 2) . Prove that the set of points in the first quadrant which are equidistant (wrt new distance) from O and A consists of the union of a line segment of finite length and an infinite ray. Sketch this set in a labelled diagram.

For points P-=(x_1,y_1) and Q-=(x_2,y_2) of the coordinates plane, a new distance d (P,Q) is defined by d(P,Q) =|x_1-x_2|+|y_1-y_2| . Let O-=(0,0) and A-=(3,2) . Consider the set of points P in the first quadrant which are equidistant (with respect to the new distance) from O and A. The area of the ragion bounded by the locus of P and the line y=4 in the first quadrant is

For points P-=(x_1,y_1) and Q-=(x_2,y_2) of the coordinates plane, a new distance d (P,Q) is defined by d(P,Q) =|x_1-x_2|+|y_1-y_2| . Let O-=(0,0) and A-=(3,2) . Consider the set of points P in the first quadrant which are equidistant (with respect to the new distance) from O and A. The set of poitns P consists of

If the line segment joining the points P(x_1, y_1)a n d Q(x_2, y_2) subtends an angle alpha at the origin O, prove that : O PdotO Q cosalpha=x_1x_2+y_1y_2dot