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What is the radius of the circle shown below x^2+y^2-8x-10y-8=0

User Galileo
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1 Answer

4 votes

Answer:

r = 7

Explanation:

equation of circle is (x - a)² + (y - b)² = r²

where a is x-coordinate of centre of circle, b is y-coordinate of centre of circle, r is the radius. radius = half of diameter.

x² - 8x + y² - 10y = 8

we need to complete the sqaure for both x and y

x² - 8x = (x - 4)² = x² - 8x + 16, which is 16 more than x² - 8x. so we need to subtract that 16.

we now have (x - 4)² - 16.

now do the same with y

(y - 5)² = y² - 10y + 25, which is 25 more than y² - 10y. so we need to subtract 25.

we now have (y - 5)² - 25.

back to our full equation.

(x - 4)² -16 + (y - 5)² - 25 = 8

(x - 4)² + (y - 5)² - 41 = 8

(x - 4)² + (y + 5)² = 49 = r²

radius r = √49 = 7

User Californian
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