Which circle among the following bisects the | vedclass

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

Question

(A) Let the given circle be $S_1: x^2+y^2-8x-6y+23=0$. The center of $S_1$ is $(4, 3)$.For a circle $S_2$ to bisect the circumference of $S_1$,the rad

Vedclass · Accepted Answer

$x^2+y^2-6x-4y+9=0$

Vedclass · Answer

(A) Let the given circle be $S_1: x^2+y^2-8x-6y+23=0$. The center of $S_1$ is $(4, 3)$.For a circle $S_2$ to bisect the circumference of $S_1$,the radical axis of $S_1$ and $S_2$ must pass through the center of $S_1$.The radical axis is given by $S_1 - S_2 = 0$.For option $A$,$S_2: x^2+y^2-6x-4y+9=0$.The radical axis is $(x^2+y^2-8x-6y+23) - (x^2+y^2-6x-4y+9) = 0$.This simplifies to $-2x - 2y + 14 = 0$,or $x + y - 7 = 0$.Substituting the center $(4, 3)$ into the radical axis equation: $4 + 3 - 7 = 0$.Since the center satisfies the equation,the circle $x^2+y^2-6x-4y+9=0$ bisects the circumference of $S_1$.

Which circle among the following bisects the circumference of the circle $x^2+y^2-8x-6y+23=0$?

Similar Questions

If the points of intersection of the ellipses $x^{2}+2y^{2}-6x-12y+23=0$ and $4x^{2}+2y^{2}-20x-12y+35=0$ lie on a circle of radius $r$ and centre $(a, b)$, then the value of $ab+18r^{2}$ is:

The radius of the circle which cuts the circles $x^2+y^2-4x-4y+7=0$,$x^2+y^2+4x-4y+6=0$,and $x^2+y^2+4x+4y+5=0$ orthogonally is

The circles $x^2 + y^2 + 2gx + 2fy = 0$ and $x^2 + y^2 + 2g'x + 2f'y = 0$ touch each other externally if:

If the circle $x^2+y^2+4x-6y+c=0$ bisects the circumference of the circle $x^2+y^2-6x+4y-12=0$,then $c$ is equal to

If the circles $x^2+y^2+2 \lambda x+2=0$ and $x^2+y^2+4y+2=0$ touch each other,then $\lambda=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module