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Write the standard equation of a circle having center (9, 1) and a point on circle at (-2, -5).

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$$(x-9)^2+(y-1)^2=(\sqrt{157} )^2.$$

Step-by-step explanation:

1. the rule is:

(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - the centre of the given circle, r - its radius.

2. using the given point (9;1) and the centre (-2;-5) it is possible to calculate 'r²':

$$r^2=(9+2)^2+(1+5)^2=157=\sqrt{157^2} .$$

3. finally,

$$(x-9)^2+(y-1)^2=\sqrt{157^2} .$$
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