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

Parabola, P_1 has focus at S(2,2) and y-axis is its directrix. Parabola, P_2 is confocal with P_1 and its directrix is x-axis. Let Q(x_1, y_1) and R(x_2, y_2) be real points of intersection of parabolas P_1a n dP_2dot If the ratio (R S)/(Q S)=a+bsqrt(b) find (a+b) (given x_2> x_1 and a , b in N)dot

For points P-=(x_1, y_1) and Q-=(x_2, y_2) of the coordinate plane, a new distance d(P ,Q)=|x_1-x_1|+|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 (with respect to the 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.

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 (a) y_1: y_2 (b) y_1: y_2 (c) x_1: x_2 (d) x_1: x_2

Find the distance between P(x_1,\ y_1)a n d\ Q(x_2, y_2) when i. P Q is parallel to the y-axis ii. PQ is parallel to the x-axis.

Planes are drawn parallel to the coordinate planes through the point P(x_1, y_1,\ z_1) and Q(x_2, y_2, z_2) . Find the length of the edges of the parallelopiped so formed.

Tangent are drawn from two points (x_1, y_1) and (x_2, y_2) to xy = c^2 . The conic passing through the two points and through the four points of contact will be circle if (A) x_1 x_2 = y_1 y_2 (B) x_1 y_2 = x_2 y_1 (C) x_1 y_2 + x_2 y_1 = 4c^2 (D) x_1 x_1 + y_1 y_2 = 4c^2

Find the scalar components and magnitude of the vector joining the points P(x_1,y_1,z_1) and Q(x_2,y_2,z_2)

Find the scalar components and magnitude of the vector joining the points P(x_1,y_1,z_1) and Q(x_2,y_2,z_2)

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