The intercepts made by the circle $x^{2} + y^{2} - 5 x - 13 y - 14 = 0$ on the x-axis and y-axis are respectively

9, 13

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5, 13

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9, 15

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None of these

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Solution

The correct option is D $9, 15$
$| x_{2} - x_{1} |, | y_{2} - y_{1} |$
When $y = 0$
$x^{2} - 5 x - 14 = 0$
$x_{1} + x_{2} 5, x_{1} x_{2} = 14$
$(x_{2} - x_{1})^{2} = 5^{2} - 4 x (- 14)$
$= 25 + 56$
$= 81$
$| x_{2} - x_{1} | = 9$
When $x_{1} = 0$
$y^{2} - 13 y - 14 = 0$
$y_{1} + y_{2} = 13, - 14 = y_{1} y_{2}$
$(y_{1} + y_{2})^{2} = (y_{1} + y_{2})^{2} - 4 y_{1} y_{2}$
$= 13^{2} - 4 x (- 14)$
$= 169 + 56$
$= 225$
$| y_{2} - y_{1} | = \sqrt{225} = 15$
$(9, 15)$

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