The circle $x^{2} + y^{2} - 14 x - 10 y + 24 = 0$ makes an

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Solution

X-intercept (y=0)
$x^{2} - 14 x + 24 = 0 x^{2} - 12 x - 2 x + 24 = 0 x (x - 12) - 2 (x - 12) = 0 (x - 12) (x - 2) = 0 x = 2 a n d x = 12 I n t e r c e p t = 12 - 2 = 10$
$A ⟶ 4$
Y-intercept (x=0)
$y^{2} - 10 y + 24 = 0 y^{2} - 6 y - 4 y + 24 = 0 y (y - 6) - 4 (y - 6) = 0 (y - 6) (y - 4) = 0 y = 6 a n d y = 4 I n t e r c e p t = 6 - 4 = 2$
$B ⟶ 2$
Intercept on Y-X
$2 x^{2} - 24 x + 24 = 0 x^{2} - 12 x + 12 = 0$
Difference of roots= $\frac{2 \sqrt{D}}{2 a} = \frac{\sqrt{D}}{a} = \frac{\sqrt{b^{2} - 4 a c}}{a} = \sqrt{{(12)}^{2} - 4 \times 12} = \sqrt{144 - 48} = 4 \sqrt{6}$
$C ⟶ 3$
(d) Intercept on $7 x - y - 4 = 0$
Centre of circle (7,5)
Radius= $\sqrt{7^{2} + 5^{2} - 24} = \sqrt{50}$

Distance of center from given line
$\frac{7 (7) + 5 - 4}{\sqrt{7^{2} + 5^{2}}} = \sqrt{50} = r a d i u s$

Hence, intercept=0

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