Circles are drown through the point (2 , 0 ) yo cut intersect of 5 units on the axis, of x . If their centres lie in the first quadrant , then prove that its equation is $x^{2} + y^{2}$ - 9 x - 2 ky + 14 = 0

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Solution

Let, the circle be g, f, c. It passes through (2, 0). $∴$ 4 + 4g + c = 0 ..(1)
Since it makes an intercept 5 on x-axis hence it must pass through (5 + 2, 0) i.e. (7, 0).
$∴$ 49 + 14g + c = 0. .(2)
Solving, 2g = -9, c = 14
There is no other relation to give the value of f.
$∴ x^{2} + y^{2}$ $- 9 x + 2 f r + 14 = 0$
where 2f is - ive as centre lies in 1st quadrant;

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Circles are drown through the point (2 , 0 ) yo cut intersect of 5 units on the axis, of x . If their centres lie in the first quadrant , then prove that its equation is x2+y2 - 9 x - 2 ky + 14 = 0

Circles are drown through the point (2 , 0 ) yo cut intersect of 5 units on the axis, of x . If their centres lie in the first quadrant , then prove that its equation is $x^{2} + y^{2}$ - 9 x - 2 ky + 14 = 0