Question

find the center and radius of the circle represented by the equation below.
$x^{2}+y^{2}+18x + 4y-15 = 0$
answer attempt 1 out of 2
center: ( , )
radius:

Explanation:

Step1: Group \(x\) and \(y\) terms

$$x^{2}+18x + y^{2}+4y=15$$

Step2: Complete the square for \(x\) terms

For \(x^{2}+18x\), \((\frac{18}{2})^{2}=81\). Add \(81\) to both sides.
$$x^{2}+18x + 81+y^{2}+4y=15 + 81$$

Step3: Complete the square for \(y\) terms

For \(y^{2}+4y\), \((\frac{4}{2})^{2}=4\). Add \(4\) to both sides.
$$x^{2}+18x + 81+y^{2}+4y+4=15 + 81+4$$

Step4: Write in standard form \((x - a)^{2}+(y - b)^{2}=r^{2}\)

$$(x + 9)^{2}+(y + 2)^{2}=100$$

Answer:

Center: \((-9,-2)\)
Radius: \(10\)