The perpendicular distance from the point to the line joining (1, 00) and (in polar coordinates) is
2
1
If D(2, 1, 0), E(2, 0, 0) and F(0, 1, 0) are mid-points of the sides BC, CA and AB of ABC, respectively. Then, the centroid ofABC is
(1, 1, 1)
(1, 1, 0)
(1, 0, 1)
(1, 2, 1)
C.
(1, 0, 1)
If the equation to the locus of points equidistant from the points (- 2, 3), (6, - 5) is ax + by + c = 0, where a > 0, then the ascending order of a, b, c is
a, b, c
c, b, a
b, c, a
a, c, b
Match the following columns.
A | The centroid of the triangle formed by (2, 3, - 1), (5, 6, 3), (2, -3 ,1) is | p | (2, 2, 2) |
B | The circumcentre of the triangle formed by (1,2, 3) (2, 3, 1), (3, 1, 2) is | q | (3, 1, 4) |
C | The orthocentre of the triangle formed by (2, 1, 5), (3, 2, 3), (4, 0, 4) is | r | (1, 1, 0) |
D | The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is | s | (3, 2, 1) |
E | The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is | t | (0, 0, 0) |
A. A B C D | (i) s p q r |
B. A B C D | (ii) p q r s |
C. A B C D | (iii) s r q r |
D. A B C D | (iv) s p t r |
A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If BAC = 90°, and ar(ABC) = 55sq. units, then the abscissa of the vertex C is :
If the point P on the curve, 4x2 + 5y2 = 20 is farthest from the point Q(0, – 4), then PQ2 is equal to :
29
48
21
36
Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC = 11 m and AB = 10 m; then the distance (in meters) of a point M on AB from the point A such that MD2 + MC2 is minimums is ___