what is the radius of the circle x^2+y^2+9x+20=0

Question

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Answer 1

You need to use "Completing the Square" to do this problem.

Group the "x's" together and put the "number" on the other side of the equal sign.

(x² + 9x ) + y² = -20

To complete the square, take half of the number that is front of the "x" (which in this case is 9), then square that number. So half of 9 is 9/2 and squaring that gives 81/4. Add that to both sides of the equation:

(x² + 9x + 81/4) + y² = -20 +81/4

Write the "x" expression as a square. The value you put with "x" will end up being half of the number that was in fron of the "x", so 9/2 in this case:

(x + 9/2)² + y² = -20 +81/4

Now add the numbers on the right side of the equal sign (you need a common denominator)

(x + 9/2)² + y² = -80/4 +81/4

(x + 9/2)² + y² = 1/4

The radius of the circle is the square root of the number on the right side of the equal sign, in this case the square root of 1/4, which is 1/2 (in other words, 1/2 x 1/2 = 1/4)

BTW, the center of the circle is (-9/2, 0) - its the negative of whatever is grouped with the x and the y