`y = x^(2) + 2x + C : y' - 2x - 2 = 0`

Let P be the point on the parabola, y^2=8x which is at a minimum distance from the centre C of the circle, x^2+(y+6)^2=1. Then the equation of the circle, passing through C and having its centre at P is : x^ 2 + y^ 2 − x + 4 y + 12 = 0 x^ 2 + y^ 2 − x/ 4 + 2 y − 24 = 0 x^ 3 + y^ 2 − 4 x + 9 y − 18 = 0 x^ 2 + y^ 2 − 4 x + 8 y + 12 = 0

The circle x^2 + y^2 - 2x - 4y + 1 = 0 and x^2 + y^2 + 4x + 4y - 1 = 0

The point (0, 0) ________ the circle x^(2) + y^(2)+2x-2y - 2 = 0 .

Show that the circles x^(2) + y^(2) + 6x + 2y + 8 = 0 and x^(2) + y^(2) + 2x + 6y + 1 = 0 intersect each other.

The equation of straight line belonging to both the families of lines (x-y+1)+lambda_1(2x-y-2)=0 and (5x+3y-2)+lambda_2(3x-y-4)=0 where lambda_1, lambda_2 are arbitrary numbers is (A) 5x -2y -7=0 (B) 2x+ 5y - 7= 0 (C) 5x + 2y -7 =0 (D) 2x- 5y- 7= 0

One of the bisector of the angle between the lines a(x-1)^2 + 2h(x-1)(y-2) + b (y-2)^2 = 0 is x + 2y - 5 = 0 . Then other bisector is (A) 2x-y=0 (B) 2x+y=0 (C) 2x+y-4=0 (D) x-2y+3=0

If the circle x^2+y^2+6x+8y+a=0 bisects the circumference of the circle x^2 + y^2 + 2x - 6y - b = 0 then (a + b) is equal to

If the points of intersection of the parabola y^(2) = 4ax and the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 are (x_(1), y_(1)) ,(x_(2) ,y_(2)) ,(x_(3), y_(3)) and (x_(4), y_(4)) respectively , then _

If the circle x^2 + y^2 + ( 3 + sin beta) x + 2 cos alpha y = 0 and x^2 + y^2 + 2 cos alpha x + 2 c y = 0 touch each other, then the maximum value of c is

Let's find value of : (x - y)a + (y - z) b + (z -x)c if a = x^2 + xy + y^2,b = y^2 + yz + z^2, c = z^2 + zx + x^2