The point on the circle `(x-3)^2 + (y-4)^2 = 4` which is at least distance from the circle `x^2 + y^2 = 1` is : (A) `(3/5, 4/5)` (B) `(9/5, 12/5)` (C) `(9, 12)` (D) none of these

The point on the parabola 4x=y^2 + 9-6y which is closest to the circle x^2 + y^2 - 10x - 10y + 49 = 0 is: (A) (9/4, 0) (B) (4, 11) (C) (1, 1) (D) none of these

The coordinates of the points on the circles x^(2) +y^(2) =9 which are at a distance of 5 units from the line 3x + 4y = 25 are :

The shortest distance of (-5,4) to the circle x^(2)+y^(2)-6x+4y-12=0 is

The coordinates of a point on the parabola y^2=8x whose distance from the circle x^2+(y+6)^2=1 is minimum is (2,4) (b) (2,-4) (18 ,-12) (d) (8,8)

If the tangents are drawn from any point on the line x+y=3 to the circle x^2+y^2=9 , then the chord of contact passes through the point. (a) (3, 5) (b) (3, 3) (c) (5, 3) (d) none of these

The nearest point on the circle x^(2)+y^(2)-6x+4y-12=0 from (-5,4) is

The point on the line (x-2)/1=(y+3)/(-2)=(z+5)/(-2) at a distance of 6 from the point (2,-3,-5) is (a). (3,-5,-3) (b). (4,-7,-9) (c). 0,2,-1 (d). none of these

The line 3x -4y = k will cut the circle x^(2) + y^(2) -4x -8y -5 = 0 at distinct points if

The shortest distance from the point (0, 5) to the circumference of the circle x^2 + y^2 - 10x + 14y - 151 = 0 is: (A) 13 (B) 9 (C) 2 (D) 5

On the ellipse 4x^2+9y^2=1, the points at which the tangents are parallel to the line 8x=9y are (a) (2/5,1/5) (b) (-2/5,1/5) (-2/5,-1/5) (d) (2/5,-1/5)