Find the equation of the circle which passes | vedclass

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

Question

(C) Let $S_1 = x^2+y^2-8x-6y+21=0$ and $S_2 = x^2+y^2-2x-15=0$. Using the family of circles equation $S_1 + \lambda S_2 = 0$,we have: $(x^2+y^2-8x-6y+

Vedclass · Accepted Answer

$3(x^2+y^2)-18x-12y+27=0$

Vedclass · Answer

(C) Let $S_1 = x^2+y^2-8x-6y+21=0$ and $S_2 = x^2+y^2-2x-15=0$. Using the family of circles equation $S_1 + \lambda S_2 = 0$,we have: $(x^2+y^2-8x-6y+21) + \lambda(x^2+y^2-2x-15) = 0$. Since the circle passes through the point $(1, 2)$,substitute $x=1$ and $y=2$ into the equation: $(1^2+2^2-8(1)-6(2)+21) + \lambda(1^2+2^2-2(1)-15) = 0$. $(1+4-8-12+21) + \lambda(1+4-2-15) = 0$. $6 + \lambda(-12) = 0$. $12\lambda = 6 \Rightarrow \lambda = \frac{1}{2}$. Substituting $\lambda = \frac{1}{2}$ back into the family equation: $(x^2+y^2-8x-6y+21) + \frac{1}{2}(x^2+y^2-2x-15) = 0$. Multiply the entire equation by $2$: $2(x^2+y^2-8x-6y+21) + (x^2+y^2-2x-15) = 0$. $2x^2+2y^2-16x-12y+42 + x^2+y^2-2x-15 = 0$. $3x^2+3y^2-18x-12y+27 = 0$. $3(x^2+y^2)-18x-12y+27 = 0$.

Find the equation of the circle which passes through the point $(1, 2)$ and the points of intersection of the circles $x^2+y^2-8x-6y+21=0$ and $x^2+y^2-2x-15=0$.

Similar Questions

Find the equation of a circle with radius $5$ units and touching the circle $x^2+y^2-2x-4y-20=0$ at the point $(5,5)$.

If the radical centre of the three circles $x^2+y^2=1$,$x^2+y^2-2x-3=0$,and $x^2+y^2-2y-3=0$ is $C(\alpha, \beta)$ and $r$ is the sum of the radii of the given circles,then the equation of the circle with $C(\alpha, \beta)$ as centre and $r$ as radius is:

If $x^2+y^2-6x-8y+12=0$ and $x^2+y^2-4x+6y+k=0$ cut orthogonally,then $k=$

The points of intersection of the circles $x^2 + y^2 = 2ax$ and $x^2 + y^2 = 2by$ are

$A$ circle passes through the origin and has its centre on $y = x$. If it cuts ${x^2} + {y^2} - 4x - 6y + 10 = 0$ orthogonally,then the equation of the circle is

Vedclass Test Series

Exam Paper Generator

Online Exam Module