A particle moves along the curve y = x2 + 2x. Then, the point on the curve such that x and y coordinates of the particle change with same rate is
(1, 3)
(- 1, - 1)
If PM is the perpendicular from P(2, 3) onto the line x + y = 3, then the coordinates of M are
(2, 1)
(- 1, 4)
(1, 2)
(4, - 1)
If OA is equally inclined to OX, OY and OZ and if A is units from the origin, then A is :
(3, 3, 3)
(- 1, 1, - 1)
(- 1, 1, 1)
(1, 1, 1)
In the triangle with vertices at A(6, 3), B(- 6, 3) and C(- 6, - 3), the median through A meets BC at P, the line AC meets the x-axis at Q, while R and S respectively denote the orthocentre and centroid of the triangle. Then the correct matching of the coordinates of points in List-I to List-II is
List-I List-II
(i) P (A) (0, 0)
(ii) Q (B) (6, 0)
(iii) R (C) (- 2, 1)
(iv) S (D) (- 6, 0)
(E) (- 6, - 3)
(F) (- 6, 3)
A. (i) (ii) (iii) (iv) | (i) D A E C |
B. (i) (ii) (iii) (iv) | (ii) D B E C |
C. (i) (ii) (iii) (iv) | (iii) D A F C |
D. (i) (ii) (iii) (iv) | (iv) B A F C |
The locus of a point such that the sum of its distances from the points (0, 2) and (0, - 2) is 6, is
9x2 - 5y2 = 45
5x2 + 9y2 = 45
9x2 + 5y2 = 45
5x2 - 9y2 = 45
The ratio in which the line joining (2, - 4, 3) and ( - 4, 5, - 6) is divided by the plane 3x + 2y + z - 4 = 0 is
2 : 1
4 : 3
- 1 : 4
2 : 3
C.
- 1 : 4