Question

Which is the equation for the circle with center (6, 2) and radius 8?

Answer 1

Answer:

$\displaystyle \boxed{ (x - 6)^2 + (y - 2)^2 = 64 }$

General Formulas and Concepts:
Precalculus

Circle Equation:
$\displaystyle (x - h)^2 + (y - k)^2 = r^2$

• (h, k) is center of circle
• r is radius

Step-by-step explanation:

Step 1: Define

Identify given.

Center (6, 2)

• h = 6
• k = 2

r = 8

Step 2: Find Equation

1. [Circle Equation] Substitute in variables:
   $\displaystyle (x - 6)^2 + (y - 2)^2 = 8^2$
2. Simplify:
   $\displaystyle (x - 6)^2 + (y - 2)^2 = 64$

∴ we have found the equation for the circle with given properties.

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Topic: Precalculus

Unit: Conics

Answer 2

The equation of a circle is  ${{x}^{2}}+{{y}^{2}}-12x-4y-24=0$.

What is circle?

A circle is a shape made up of all points in a plane that are at the same distance from a central point.

Equation of the circle $\[{{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}\]$ where (h,k) is the coordination of the center and r is the radius

Which is the equation for the circle with center (6, 2) and radius 8?

put the values of h, k and r in the equation of the circle

${{\left( x-6 \right)}^{2}}+{{\left( y-2 \right)}^{2}}={{8}^{2}}$

${{x}^{2}}+{{y}^{2}}+36+4-12x-4y=64$

${{x}^{2}}+{{y}^{2}}-12x-4y-24=0$

therefore, the equation of the circle is${{x}^{2}}+{{y}^{2}}-12x-4y-24=0$.

Learn more about cone here – https://brainly.com/question/11833983

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