Let `C_1` and `C_2` be respectively, the parabolas `x^2=y-1` and `y^2=x-1` Let P be any point on `C_1` and Q be any point on `C_2` . Let `P_1` and `Q_1` be the refelections of P and Q, respectively with respect to the line y=x.
Arithemetic mean of `PP_1`and `Q Q_1` is always less than

Let C_1 and C_2 be respectively, the parabolas x^2=y-1 and y^2=x-1 Let P be any point on C_1 and Q be any point on C_2 . Let P_1 and Q_1 be the refelections of P and Q, respectively with respect to the line y=x. If the point p(pi,pi^2+1) and Q(mu^2+1,mu) then P_1 and Q_1 are

Let C_1 and C_2 be parabolas x^2 = y - 1 and y^2 = x-1 respectively. Let P be any point on C_1 and Q be any point C_2 . Let P_1 and Q_1 be the reflection of P and Q, respectively w.r.t the line y = x then prove that P_1 lies on C_2 and Q_1 lies on C_1 and PQ >= [P P_1, Q Q_1] . Hence or otherwise , determine points P_0 and Q_0 on the parabolas C_1 and C_2 respectively such that P_0 Q_0 <= PQ for all pairs of points (P,Q) with P on C_1 and Q on C_2

let P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is

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

P and Q are two distinct points on the parabola, y^2 = 4x with parameters t and t_1 respectively. If the normal at P passes through Q , then the minimum value of t_1 ^2 is

Let P be a point on the curve c_(1):y=sqrt(2-x^(2)) and Q be a point on the curve c_(2):xy=9, both P and Q be in the first quadrant. If d denotes the minimum distance between P and Q, then d^(2) is ………..

A line intersects the Y- axis and X-axis at the points P and Q, respectively. If (2,-5) is the mid- point of PQ, then the coordinates of P and Q are, respectively.

Q is the image of point P(1, -2, 3) with respect to the plane x-y+z=7 . The distance of Q from the origin is.

In a triangle A B C , let P and Q be points on AB and AC respectively such that P Q || B C . Prove that the median A D bisects P Q .

Let P and Q be two points on the curves x^2+y^2=2 and (x^2)/8+y^2/4 =1 respectively. Then the minimum value of the length PQ is