If one of the diameters of the circle, given by the equation, x2 + y2 - 4x + 6y - 12 = 0, is a chord of a circle S , whose centre is at (-3, 2), then the radius of S is :

Question

If one of the diameters of the circle, given by the equation, x2 + y2 - 4x + 6y - 12 = 0, is a chord of a circle S , whose centre is at (-3, 2), then the radius of S is : (A)  5√2 (B)  5√3 (C) 5 (D) 10

Tardigrade Admin · Accepted Answer

x2+y2-4 x+6 y-12=0 Centre (2,-3) Radius √4+9+12=5 Distance b / w two centres c1(2,-3) and c2(-3,2) d=√(2+3)2+(-3-2)2=√50 Radius of ( S )=√52+(√50)2=√75=5 √3

Q. If one of the diameters of the circle, given by the equation, $x^{2} + y^{2} - 4 x + 6 y - 12 = 0$ , is a chord of a circle $S$ , whose centre is at $(- 3, 2)$ , then the radius of $S$ is :

$52$

$53$

5

10

$x^{2} + y^{2} - 4 x + 6 y - 12 = 0$
Centre $(2, - 3)$
Radius $4 + 9 + 12 = 5$
Distance $b / w$ two centres $c_{1} (2, - 3)$ and $c_{2} (- 3, 2)$
$d = (2 + 3)^{2} + (- 3 - 2)^{2} = 50$
Radius of $(S) = 5^{2} + (50)^{2} = 75 = 53$

Q. If one of the diameters of the circle, given by the equation,x2+y2−4x+6y−12=0, is a chord of a circle S , whose centre is at (−3,2), then the radius of S is :

52​

53​

5

10

x2+y2−4x+6y−12=0 Centre (2,−3) Radius 4+9+12​=5 Distance b/w two centres c1​(2,−3) and c2​(−3,2) d=(2+3)2+(−3−2)2​=50​ Radius of (S)=52+(50​)2​=75​=53​

Q. If one of the diameters of the circle, given by the equation, $x^{2} + y^{2} - 4 x + 6 y - 12 = 0$ , is a chord of a circle $S$ , whose centre is at $(- 3, 2)$ , then the radius of $S$ is :

$52$

$53$

$x^{2} + y^{2} - 4 x + 6 y - 12 = 0$
Centre $(2, - 3)$
Radius $4 + 9 + 12 = 5$
Distance $b / w$ two centres $c_{1} (2, - 3)$ and $c_{2} (- 3, 2)$
$d = (2 + 3)^{2} + (- 3 - 2)^{2} = 50$
Radius of $(S) = 5^{2} + (50)^{2} = 75 = 53$