Find the x-intercept of the circle x^2 + y^2 | vedclass

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(A) The equation of the circle is $x^2 + y^2 + 4x - 7y - 12 = 0$.To find the $x$-intercept,we set $y = 0$ in the equation of the circle.Substituting $

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$8$

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(A) The equation of the circle is $x^2 + y^2 + 4x - 7y - 12 = 0$.To find the $x$-intercept,we set $y = 0$ in the equation of the circle.Substituting $y = 0$ into the equation,we get $x^2 + 0^2 + 4x - 7(0) - 12 = 0$,which simplifies to $x^2 + 4x - 12 = 0$.Factoring the quadratic equation,we have $(x + 6)(x - 2) = 0$.This gives the roots $x = -6$ and $x = 2$.The points where the circle intersects the $x$-axis are $(-6, 0)$ and $(2, 0)$.The $x$-intercept is the distance between these two points,which is $|2 - (-6)| = |2 + 6| = 8$.

Find the $x$-intercept of the circle $x^2 + y^2 + 4x - 7y - 12 = 0$.

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