Rewrite the Equation in Standard Form $$x ^ { 2 } + y ^ { 2 } - 12 y + 20 = 0$$

question 49

Multiple Choice

Rewrite the equation in standard form. Find the center and radius of the circle.
- $$x ^ { 2 } + y ^ { 2 } - 12 y + 20 = 0$$

• A) \(x ^ { 2 } + ( y + 6 ) ^ { 2 } = 16\)
• center \(( 0 , - 6 ) , \mathrm { r } = 4\)
• B) \(x ^ { 2 } + ( y - 6 ) ^ { 2 } = 16\)
• center \(( 0,6 ) , \mathrm { r } = 4\)
• C) \(( x - 6 ) ^ { 2 } + y ^ { 2 } = 16\)
• center \(( 6,0 ) , \mathrm { r } = 4\)
• D) \(x ^ { 2 } + ( y - 6 ) ^ { 2 } = 16\)
• center \(( 0 , - 6 ) , \mathrm { r } = 4\)

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Definitions:

Relative Height

A principle in visual perception where objects positioned higher in the visual field are perceived as more distant.

Linear Perspective

A technique in art and photography that creates the illusion of depth on a flat surface by converging lines at a single point.

Moon Illusion

A perceptual phenomenon in which the Moon appears larger near the horizon than it does while higher up in the sky.

Perceived Distance

The subjective estimation or impression of the space between oneself and an object or between two points.