The radius of the larger circle lying in the first quadrant and touching the line 4x + 3y - 12 =0 and the co-ordinate axes,is
5
6
7
8
B.
6
Let the equation of the circle is
x2 + y2 + 2gx +2fy +c =0
Thus circle touch the coordinate axes and lying in the first quadrant, then
g2 - c =0 and f2 - c = 0
The parabola with directrix x + 2y - 1 = 0 and focus (1, 0) is
4x2 - 4xy + y2 - 8x + 4y + 4 = 0
4x2 + 4xy + y2 - 8x + 4y + 4 = 0
4x2 + 5xy + y2 + 8x - 4y + 4 = 0
4x - 4xy + y - 8x - 4y + 4 = 0
A.
4x2 - 4xy + y2 - 8x + 4y + 4 = 0
Let P(x, y) be any point on the parabola
By defination of Parabola PM = PS
Let M be the foot of the perpendicular from a point P on the parabola y = 8(x - 3) onto its directrix and let S be the focus ofthe parabola. If SPM is an equilateral triangle, then P is equal to
C.
Let coordinate of P (h + at2, k + 2at) = P(3 + 2t2, 4t)
Then, coordinate of M(- 5, 4t)
We know that the side of this equilateral trianle is 4a = 4 x 2 = 8
Now, PS = 8
The length of the common chord of the circles of radii 15 and 20, whose centres are 25 unit of distance apart, is
12
16
24
25
C.
24