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The equation of a circle is shown. What is the radius? 22 + y2 - 10x + 8y + 16 = 0​

2 Answers

11 votes

Answer:

radius = 5

Explanation:

Given

  • x² + y² - 10x + 8y + 16 = 0

Using completing the square method

  • x² - 10x + 25 - 25 + y² + 8y + 16
  • (x + 5)² + (y + 4)² - 25 = 0
  • (x + 5)² + (y + 4)² = 25

Standard form for equation of a circle

  • (x - h)² + (y - k)² = r², where r is the radius

On comparison to our equation in the question :

  • r² = 25
  • radius = 5 [as distances cannot be -ve]

User David Tuite
by
8.4k points
3 votes

Answer:

radius = 5

Explanation:

Question


x^2+y^2-10x+8y+16=0

The equation of a circle is shown. What is the radius?

----------------------------------------------------------------------------------

Equation of a circle


(x-a)^2+(y-b)^2=r^2

(where (a, b) is the center and r is the radius)

Given equation:


x^2+y^2-10x+8y+16=0

Collect like terms:


\implies x^2-10x+y^2+8y+16=0

Subtract 16 from both sides:


\implies x^2-10x+y^2+8y=-16

Complete the square for both variables.

Add 25 to both sides for x. Add 16 to both sides for y.


\implies x^2-10x+25+y^2+8y+16=-16+25+16


\implies (x^2-10x+25)+(y^2+8y+16)=25

Factor the two variables:


\implies (x-5)^2+(y+4)^2=25

Therefore:

  • center of the circle = (5, -4)
  • radius of the circle = √25 = 5
User VanHoesel
by
8.6k points

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