Question

find the centre and radios of circle2(x+1)^2+ 2y^2=25

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HOMEWORK HELP > MATH

Find the centre and radius of the circle:x^2 + y^2 + 8x + 6y= 0  

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EXPERT ANSWERS

HALA718 | CERTIFIED EDUCATOR

x^2 + y^2 + 8x + 6y= 0

We need to re-write the equation in the following format:

( x- a)^2 + ( y-b)^2 = r^2   such that:

(a,b) is the center of the circle and r is the radius:

Let us calculate:

We will re-arrange terms:

x^2 + 8x + y^2 + 6y = 0

We will complete the squares:

==> ( x+4)^2 - 16 + ( y+3)^2 - 9 = 0

==> ( x+4)^2 + ( y+3)^2 - 25 = 0

We will move 25 to the right side:

==> ( x+ 4)^2 + ( y+3)^2 = 25

==> ( x+ 4)^2 + ( y+3)^2 = 5^2

Now the equation is in the standard form:

Then the center of the circle is ( -4, -3) and the radius = 5