Find the equation of the circle of radius 5 cm, whose centre lies on the lies on the y-axis and which passes through the point ` (3, 2 )`

Find the equation of the circle of radius 5 cm, whose centre lies on t

1.	Find the equation of the circle of radius 5 cm, whose centre lies on the lies on the y-axis and which passes through the point ` (3, 2 )`
Answer» Correct Answer - ` (x ^(2) + y ^(2) - 12y + 11 =0 ) or (x ^(2) + y ^(2) + 4y - 21=0 )` Let the centre of the circle be `C( 0, k)` It is given that the circle passes through ` P(3, 2)` Then `, \|CP\|^(2) = 5^(2) hArrf (0 - 3) ^(2) + ( 2 - k ) ^(2) = 5^(2)` `" " hArr ( 2- k ) = pm 4 hArr k = 6 or k = - 2 ` ` therefore ` the centre of the circles is ` (0, 6) or (0, - 2 )` Hence, the equation of the circle is ` " "[(x - 0) ^(2) + ( y - 6) ^(2) = 5^(2) ] or [ ( x - 0 ) ^(2) + (y + 2 ) ^(2) = 5 ^(2) ] `.

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Find the equation of the circle of radius 5 cm, whose centre lies on the lies on the y-axis and which passes through the point ` (3, 2 )`

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