QuestionIdentify the center and radius of these circles: 1. $x^{2}+y^{2}=49$ 2. $5(x^{2}+y^{2})=125$ 3. $(x+4)^{2}+(y-2)^{2}=9$. Find standard forms for: 4. center at origin, radius $5\sqrt{3}$ 5. center $(17,5)$, radius 12 6. center $(-8,4)$, contains $(-4,2)$ 7. center $(15,7)$, tangent to $x$-axis.

Studdy Solution
For the seventh problem, we are given the center at $(15,7)$ and that the circle is tangent to the x-axis. A circle is tangent to the x-axis at its center, so the radius is the y-coordinate of the center.
$$Radius =7$$The standard form of the equation is$$(x-15)^{2}+(y-7)^{2}=7^{2}$$which simplifies to$$(x-15)^{2}+(y-7)^{2}=49$$