Which equation could represent a circle with a center located at (11,-5)

1 answer:

6 0

The standard equation of a circle is:

$(x-h)^2-(y-k)^2=r^2$ where (h,k) is the center and r is the radius.

We need to make an equation of a circle, whose center is (11,-5) with any radius. Therefore, substitute the value.

$(x-h)^2-(y-k)^2=r^2 \\ (11,-5)=(h,k) \\ (x-11)^2-(y-5)^2=64$

The bolded part is your answer. Since the radius is not given, we can put any value.

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$\huge{\boxed{y=-\frac{5}{6} x+4}}$

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Point-slope form is $y-y_1=m(x-x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is any known point on the line.

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