Question

question 9, 2.4.37 part 2 of 4 a circle has the equation 2x² + 24x + 2y² = 0. (a) find the center (h,k) and radius r of the circle. (b) graph the circle. (c) find the intercepts, if any, of the graph. (a) the center of the circle is (-6,0). (type an ordered pair, using integers or decimals.) the radius of the circle is . (type an integer or a decimal.)

Explanation:

Step1: Rewrite the given equation

First, divide the entire equation $2x^{2}+24x + 2y^{2}=0$ by 2 to get $x^{2}+12x + y^{2}=0$.

Step2: Complete the square for the x - terms

The coefficient of $x$ is 12. Half of it is 6, and its square is 36. Add 36 to both sides of the equation: $x^{2}+12x + 36+y^{2}=36$.

Step3: Write in standard form

The standard - form of a circle's equation is $(x - h)^{2}+(y - k)^{2}=r^{2}$. The equation $x^{2}+12x + 36+y^{2}=36$ can be written as $(x + 6)^{2}+y^{2}=36$, which is in the standard form $(x-(-6))^{2}+(y - 0)^{2}=6^{2}$.

Answer:

6