Question

a circle is centered at the origin and contains the point (4,0). Would (2 square root 2,-square root 6) also be on the circle

Answer 1

circle do not contains point (2√2 , -6)

Explanation:

Equation of circle:

The centre-radius form of the circle equation is in the format

(x – h)² + (y – k)² = r²

with the centre being at the point (h, k) and the radius being "r"

Plug in values given the question to find the radius of circle

(4-0)² + (0 - 0)² = r²

r² = 16

r = √16

r = 4

To find coordinates(2√2 , -6) is in the circle

Simply plug in the x and y from your point (2√2 , -6)

If the the answer is greater than r², then the point lies outside of the circle else they are in the circle

(x – 0)² + (y – 0)² ≤ 16

((2√2)² – 0)² + ((-6)² – 0)² ≤ 16

8 + 36 ≤ 16

44 ≤ 16 False

Hence, (2√2 , -6) don't lie in or on the circle.