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eimsori [14]
3 years ago
12

Explain How you got that answer

Mathematics
1 answer:
Studentka2010 [4]3 years ago
5 0

Answer:

\huge\boxed{Center= (-3,4) , Radius = 5\sqrt{2} }

Step-by-step explanation:

<u><em>Given equation is </em></u>

<u><em></em></u>x^2 + y^2 + 6x-8y - 25 = 0

Adding 25 to both sides

x^2 + y^2 +6x-8y = 25

Completing squares

x^2 +6x +y^2 - 8y = 25\\(x)^2-2(x)(-3) + (y)^2 - 2(x)(4) = 25

Both of their "b" is -3 and 4 respectively

So, adding (-3)² => 9 and (4)² => 16 to both sides

(x+3)^2 + (y-4)^2 = 25 + 9 + 16\\(x+3)^2 + (y-4)^2 = 50\\(x-(-3))^2 + (y-4)^2 = (5\sqrt{2)^2}

Comparing it with (x-h)^2+(y-k)^2 = r^2, where center = (h,k) and radius = r.

We get:

Center = (-3,4)

Radius = 5\sqrt{2}

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