Answered

The equation of the circle is x2 + y2 + 8x - 6y – 24 = 0. What is its center?

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SOLUTION

Given that x²+y²+8x-6y-24=0

We will transform the general form to its standard form

  • x²+y²+8x-6y-24=0

We will group the like terms

  • x²+8x+y²-6y = 24

Now , make the grouped terms to a perfect square trinomial

  • x²+8x+16+y²-6y+9 = 24 + 16 + 9

Note that when adding on the left side of the equation , you should add also on the right

  • x²+8x+16 + y²-6y+9 = 50

We will make the perfect square trinomial in factored form

  • (x+4)²+(y-3)²=50

Here , We will find its center and radius

  • (x-h)²+(y-k)²=r²
  • (x-(-4))²+(y-(3))²=√50
  • (x-(-4))²+(y-(3))²=5√2

Thus , We can see that the center is (-4,3) and radius of 5√2 units

ANSWER

  • The Center is at (-4,3)
  • The radius is 5√2 units

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