A circle passes through the point (-1, 0) and | vedclass

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(D) Let the center of the circle be $(h, k)$.Since the circle touches the $y$-axis at $(0, 2)$,the radius $r = |h|$ and the $y$-coordinate of the cent

Vedclass · Accepted Answer

$(-4, 0)$

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(D) Let the center of the circle be $(h, k)$.Since the circle touches the $y$-axis at $(0, 2)$,the radius $r = |h|$ and the $y$-coordinate of the center $k = 2$.Thus,the equation of the circle is $(x - h)^2 + (y - 2)^2 = h^2$.Since the circle passes through $(-1, 0)$,we substitute these coordinates into the equation:$(-1 - h)^2 + (0 - 2)^2 = h^2$$1 + 2h + h^2 + 4 = h^2$$2h + 5 = 0$$h = -5/2$.So,the equation of the circle is $(x + 5/2)^2 + (y - 2)^2 = (-5/2)^2$.$(x + 5/2)^2 + (y - 2)^2 = 25/4$.Now,check the options by substituting the points into the equation:For $(-4, 0)$:$(-4 + 5/2)^2 + (0 - 2)^2 = (-8/2 + 5/2)^2 + (-2)^2 = (-3/2)^2 + 4 = 9/4 + 4 = 25/4$.Since the point $(-4, 0)$ satisfies the equation,the circle passes through $(-4, 0)$.

$A$ circle passes through the point $(-1, 0)$ and touches the $y$-axis at $(0, 2)$. Through which other point does this circle pass?

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