## Related questions with answers

Question

Write an equation for a circle that satisfies each set of conditions. Then graph the circle. center at (-4,-3), tangent to y=3

Solution

VerifiedStep 1

1 of 2The standard form of the equation of a circle with center $(h,k)$ and radius $r$ is given by:

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

We are given $(h,k)=(-4,-3)$. If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. The distance between $(-4,-3)$ and $y=3$ is $|-3-3|=6$ so $r=6$:

$(x-(-4))^2+(y-(-3))^2=6^2$

$\color{#c34632}(x+4)^2+(y+3)^2=36$

To graph, locate the center first and use the radius to identify other points $r$ units to the left, right, above, and below the center:

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