बिंदु (-1, 2) से वृत्त S_(1) -= x^(2) + y^(2) + 6y + 7 = 0 तथा S_(2) -= x^(2) + y^(2) + 6x + 1 =...

If P_(1), P_(2), P_(3) are the perimeters of the three circles. S_(1) : x^(2) + y^(2) + 8x - 6y = 0 S_(2) , 4x^(2) + 4y^(2) -4x - 12y - 186 = 0 and S_(3) : x^(2) + y^(2) -6x + 6y - 9 = 0 repeectively, then the relation amongst P_(1), P_(2) and P_(3) is .............

Number of common tangents to the circles C_(1):x ^(2) + y ^(2) - 6x - 4y -12=0 and C _(2) : x ^(2) + y ^(2) + 6x + 4y+ 4=0 is

Let C_(1) and C_(2) be the circles x^(2) + y^(2) - 2x - 2y - 2 = 0 and x^(2) + y^(2) - 6x - 6y + 14 = 0 respectively. If P and Q are points of intersection of these circles, then the area (in sq. units ) of the quadrilateral PC_(1) QC_(2) is :

The equation (s) of common tangents (s) to the two circles x^(2) + y^(2) + 4x - 2y + 4 = 0 and x^(2) + y^(2) + 8x - 6y + 24 = 0 is/are

The centres of the circles x ^(2) + y ^(2) =1, x ^(2) + y^(2)+ 6x - 2y =1 and x ^(2) + y^(2) -12 x + 4y =1 are

Radii of circles x^(2) + y^(2) = 1, x^(2) + y^(2) - 2x - 6y= 6 and x^(2) + y^(2) - 4x - 12y = 9 are in

I. 12x^(2) + 17x+ 6 = 0" " II. 6y^(2) + 5y + 1 = 0

y-1=m_1(x-3) and y - 3 = m_2(x - 1) are two family of straight lines, at right angled to each other. The locus of their point of intersection is: (A) x^2 + y^2 - 2x - 6y + 10 = 0 (B) x^2 + y^2 - 4x - 4y +6 = 0 (C) x^2 + y^2 - 2x - 6y + 6 = 0 (D) x^2 + y^2 - 4x - by - 6 = 0

I. 3x^(2) + 7x = 6 " " II. 6(2y^(2)+1) = 17 y

6x + 5y = 7x + 3y + 1 = 2 ( x + 6y - 1 )