Given a circle has two of its diameter as 2x y 6 amp 3x 2y 4 also circle passes through point 6 7 fi...........

Quantitative Aptitude (CDS) Coordinate Geometry

Given a circle has two of its diameter as 2x+y=6 & 3x+2y=4 also circle passes through point ( 6, - 7 ) find the equation of the circle .

x²+y²+5x-52y-31=0

x²+y²+5x-21y-16=0

x²+y²+16x+20y+51=0

x²+y²+5x-25y-23=0

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Explanation:

equation of the circle having centre ( h,k ) & radius r is given by
(x-h)²+(y-k)²=r²
On solving 2x+y=6 & 3x+2y=4
We get centre as ( 8, - 10 ) & radius r = distance between centre and the given point
Distance between two points = √( x1 - x2 )² + (y1-y2)²
= √13
Putting these values in the equation of circle and we get
x²+y²+16x+20y+51=0