Find the standard form of the equation of the circle with center (-5,4) and tangent to the line y=2

(x + 5)^2 + (y - 4)^2 = 2^2

Step-by-step explanation:

The standard form of the equation of a circle of center (h, k) and radius r

is (x - h)^2 + (y - k)^2 = r^2.

Here the tangent line is y = 2.  This is a horizontal line.  The point of tangency has the same x-coordinate as does the center (-5, 4); that is, this point is (-5, 2).  These two facts tell us that the radius of the circle is (4 - 2), or 2.

Filling in the knowns h = -5, k = 2 and r = 2, we get the equation of this circle:

(x + 5)^2 + (y - 4)^2 = 2^2

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step-by-step explanation:

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