The line segment joining the points (4, 7) and $( - 2,\ - 1)$ is a dismeter of a circle. If the circle intersects the $x$-axis at $A$ and $B$, then $AB$ is equal to

Question

Dr. Abubacker · Accepted Answer

(d)
Equation of circle is
$(x - 4)(x + 2) + (y - 7)(y + 1) = 0$
$\Rightarrow x^{2} - 2x - 8 + y^{2} + y - 7y - 7 = 0$
$\Rightarrow x^{2} + y^{2} - 2x - 6y - 15 = 0$
Here, $g = - 1,\ c = - 15$
$	herefore\ \ AB = 2\sqrt{g^{2} - c}$
$= 2\sqrt{1 + 15}$
$= 8$

Q. The line segment joining the points (4, 7) and $( - 2,\ - 1)$ is a dismeter of a circle. If the circle intersects the $x$-axis at $A$ and $B$, then $AB$ is equal to

Explanation

Reviewed by Dr. Abubacker

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