Question

Find the centre of a circle passing through (5,-8), (2,-9) and (2,1)

Answer 1

$\textbf{Given:}$

$\text{Circle passes through (5,-8), (2,-9) and (2,1) }}$

$\textbf{To find:}$

$\text{Centre of the circle}$

$\textbf{Solution:}$

$\text{Let the equation of the required circle be}$

$x^2+y^2+2g\,x+2f\,y+c=0$

$\text{Since the circle passes through (5,-8),}$

$5^2+(-8)^2+2g(5)+2f(-8)+c=0$

$25+64+10\,g-16\,f+c=0$

$10\,g-16\,f+c=-89$.....(1)

$\text{Since the circle passes through (2,-9),}$

$2^2+(-9)^2+2g(2)+2f(-9)+c=0$

$4+81+4\,g-18\,f+c=0$

$4\,g-18\,f+c=-85$.....(2)

$\text{Since the circle passes through (2,1),}$

$2^2+1^2+2g(2)+2f(1)+c=0$

$4+1+4\,g+2\,f+c=0$

$4\,g+2\,f+c=-5$.....(3)

$\text{Subtract (2) from (1), we get}$

$6\,g+2\,f=-4$

$\implies\,3\,g+f=-2$......(4)

$\text{Subtract (3) from (2), we get}$

$-20\,f=-80$

$\implies\boxed{\bf\,f=4}$

$\text{Put f=4 in (4), we get}$

$3\,g+4=-2$

$3\,g=-6$

$\implies\boxed{\bf\,g=-2}$

$\text{Centre of the circle is}$

$(-g,-f)$

$(2,-4)$

$\therefore\boxed{\textbf{Centre of the required circle is (2,-4)}}$

Find more:

Find the equation of the circle passing through the points (1,2),(3,-4)and (5,-6)find the centre and rafius in each case

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Find the equation of circle which passes through points (5,-8),(2,-9) and(2,1). Find also the coordinates of its centre and radius

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Answer 2

Answer:

you can check in all in one guide cbse class 10