Circles are drawn through the point $(2, 0)$ to cut an intercept of length $5$ units on the x-axis. If their centre lie in the first quadrant, then their equation is

x^{2} + y^{2} - 9 x + 2 k y + 14 = 0, k \in R^{+}

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3 x^{2} + 3 y^{2} + 27 x - 2 k y + 42 = 0, k \in R^{+}

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x^{2} + y^{2} - 9 x - 2 k y + 14 = 0, k \in R^{+}

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x^{2} + y^{2} - 2 k x - 9 y + 14 = 0, k \in R^{+}

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Solution

The correct option is B $x^{2} + y^{2} - 9 x - 2 k y + 14 = 0, k \in R^{+}$
It is clear from the figure that the co-ordinates of the centre of such circles are $(\frac{9}{2}, k)$
$∴$ Equation of such circles is ${(x - \frac{9}{2})}^{2} + {(y - k)}^{2}$
$= {(2 - \frac{9}{2})}^{2} + {(k - 0)}^{2} = \frac{25}{4} + k^{2}$
or $x^{2} + y^{2} - 9 x - 2 k y + 14 = 0$

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