Home
Class 11
MATHS
Let C1 and C2 be parabolas x^2 = y - 1 a...

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`

Promotional Banner

Similar Questions

Explore conceptually related problems

Let E be the ellipse (x^2)/9+(y^2)/4=1 and C be the circle x^2+y^2=9 . Let Pa n dQ be the points (1, 2) and (2, 1), respectively. Then (a) Q lies inside C but outside E (b) Q lies outside both Ca n dE (c) P lies inside both C and E (d) P lies inside C but outside E

If a point Q lies between two points P and R such that PQ = QR, prove that PQ = 1/2 PR.

Let O be the origin and A be the point (64,0). If P, Q divide OA in the ratio 1:2:3, then the point P is

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

Let C_1 and C_2 are circles defined by x^2+y^2 -20x+64=0 and x^2+y^2+30x +144=0 . The length of the shortest line segment PQ that is tangent to C_1 at P and to C_2 at Q is

Let O be the vertex and Q be any point on the parabola, x^2=""8y . It the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

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

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

Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that a/p(q-r)+b/q (r-p) +c/r (p-q)=0