If a diameter of the circle x^2+y^2-4x+6y-12= | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given circle is $x^2+y^2-4x+6y-12=0$.Comparing with $x^2+y^2+2gx+2fy+c=0$,we get $g=-2$,$f=3$,and $c=-12$.The centre $C$ of this circle is $(-

Vedclass · Accepted Answer

$5 \sqrt{3}$

Vedclass · Answer

(A) The given circle is $x^2+y^2-4x+6y-12=0$.Comparing with $x^2+y^2+2gx+2fy+c=0$,we get $g=-2$,$f=3$,and $c=-12$.The centre $C$ of this circle is $(-g, -f) = (2, -3)$ and its radius $r$ is $\sqrt{g^2+f^2-c} = \sqrt{(-2)^2+(3)^2-(-12)} = \sqrt{4+9+12} = \sqrt{25} = 5$.Let $O(-3, 2)$ be the centre of circle $S$. The diameter of the first circle is a chord of circle $S$.The distance $d$ between the centres $O(-3, 2)$ and $C(2, -3)$ is $d = \sqrt{(2 - (-3))^2 + (-3 - 2)^2} = \sqrt{5^2 + (-5)^2} = \sqrt{25+25} = \sqrt{50} = 5\sqrt{2}$.In the right-angled triangle formed by the centre of $S$,the centre of the first circle,and a point on the chord,the radius $R$ of circle $S$ is given by $R^2 = r^2 + d^2$.$R^2 = 5^2 + (5\sqrt{2})^2 = 25 + 50 = 75$.$R = \sqrt{75} = 5\sqrt{3}$.

If a diameter of the circle $x^2+y^2-4x+6y-12=0$ is a chord of a circle $S$ whose centre is at $(-3, 2)$,then the radius of $S$ is

Similar Questions

The equation of the circle passing through the points of intersection of the circles $x^2+y^2+6x+4y-12=0$ and $x^2+y^2-4x-6y-12=0$ and having radius $\sqrt{13}$ is

The radical axis of the co-axial system of circles with limiting points $(1, 2)$ and $(-2, 1)$ is

If the circles $x^2+y^2-4x+6y+13-a^2=0$ and $x^2+y^2-10x-2y+17=0$ intersect in two distinct points,then '$a$' is

The limiting points of the co-axial system containing the two circles $x^2+y^2+2x-2y+2=0$ and $25(x^2+y^2)-10x-80y+65=0$ are

$(a, 0)$ and $(b, 0)$ are centers of two circles belonging to a coaxial system of which the $y$-axis is the radical axis. If the radius of one of the circles is $r$,then the radius of the other circle is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module