Question
Find the general equation of a circle centre (1,4),radius 3units
Question 7Select one:
x2+y2-x-4y+4=0
x2+y2-3x+4y-5=0
x2+y2-2x-8y+8=0
x2+y2-4x+16y+10=0
Question 7Select one:
x2+y2-x-4y+4=0
x2+y2-3x+4y-5=0
x2+y2-2x-8y+8=0
x2+y2-4x+16y+10=0
Answers
GPT 3.5
The general equation of a circle with center (h, k) and radius r is:
(x - h)² + (y - k)² = r²
Plugging in the given values, we get:
(x - 1)² + (y - 4)² = 3²
(x - 1)² + (y - 4)² = 9
Expanding this equation gives:
x² - 2x + 1 + y² - 8y + 16 = 9
x² + y² - 2x - 8y + 17 = 9
x² + y² - 2x - 8y + 8 = 0
Therefore, the correct answer is: x² + y² - 2x - 8y + 8 = 0.
(x - h)² + (y - k)² = r²
Plugging in the given values, we get:
(x - 1)² + (y - 4)² = 3²
(x - 1)² + (y - 4)² = 9
Expanding this equation gives:
x² - 2x + 1 + y² - 8y + 16 = 9
x² + y² - 2x - 8y + 17 = 9
x² + y² - 2x - 8y + 8 = 0
Therefore, the correct answer is: x² + y² - 2x - 8y + 8 = 0.