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mafiozo [28]
3 years ago
13

Find the radius of the circle with equation x^2 + y^2 - 10x - 16y + 53 = 0.

Mathematics
1 answer:
olga55 [171]3 years ago
6 0

Answer:

<h2>radius = 10.5 units</h2>

Step-by-step explanation:

Equation of a circle is given by

x² + y² + 2gx + 2fy + c = 0

To find the radius of the circle we use the formula

r =  \sqrt{ {g}^{2}  +  {f}^{2} - c }

where g and f is the center of the circle

From the question

x² + y² - 10x - 16y + 53 = 0

Comparing with the general equation above we have

2g = - 10 2f = - 16

g = - 5 f = - 8

c = 53

Substitute the values into the above formula

That's

r =  \sqrt{ ({ - 10})^{2}  + ( { - 8})^{2} - 53 }

r =  \sqrt{100 + 64 - 53}

r =  \sqrt{111}

We have the final answer as

<h3>radius = 10.5 units</h3>

Hope this helps you

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