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lys-0071 [83]
3 years ago
10

Find the coordinates of the circle and the radius y²+2x+x²-24y= -120

Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
3 0
We know that
the equation of a circle is
(x-h+(y-k)²=r²
where (k,k)----> is the center
and
r----> is the radius
y²+2x+x²-24y= -120

Group terms that contain the same variable
 (y²-24y)+(x²+2x)=-120

Complete the square twice. Remember to balance the equation by adding the same constants to each side
 (y²-24y+144)+(x²+2x+1)=-120+144+1

<span>Rewrite as perfect squares</span>

(y-12)²+(x+1)²=25

(x+1)²+(y-12)²=5²

the answer is
the coordinates of the center are (-1,12)
the radius is 5 units
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Step-by-step explanation:

Let the points A, B, C and S represent Alba, Blare, Cray and Service station respectively,

Then According to the question,

We have to find out the line segment CS = x = ?

Now, In the triangles ACB and CSB,

\angle ACB\cong \angle CSB     ( Right angles )

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Thus, by AA similarity postulate,

\triangle ACB\sim\triangle CSB

By the property of similar triangles,

\frac{AB}{CB}=\frac{AC}{CS}

\implies \frac{50}{30}=\frac{40}{x}

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