if the coordinates of the centre of a circle are (5,a) and two points on the circle are (9,1) and (5,5) then find the area of the circle
Answers
Answer:
π/16 sq units as radius = 1/4.
Step-by-step explanation:
Given the center O = (5, a).
Two points on the circle are: A(9,1) and B(5,5).
Generic equation of a circle: (x - p)² + (y - q)² = r²
where , (p,q) is the center and r is the radius.
Radius = r = OA = OB.
So r² = OA² = OB²
(9-5)² + (a-1)² = (5-5)² + (a -5)² = r²
a² -2 a + 17 = a² - 10 a + 25 = r²
=> 8 a = 42
=> a = 21/4 = 5.25.
So r² = (a -5)² = 1/16
r = 1/4
So the circle area = π r² = π /16 sq units.
Answer:
Answer:
π/16 sq units as radius = 1/4.
Step-by-step explanation:
Given the center O = (5, a).
Two points on the circle are: A(9,1) and B(5,5).
Generic equation of a circle: (x - p)² + (y - q)² = r²
where , (p,q) is the center and r is the radius.
Radius = r = OA = OB.
So r² = OA² = OB²
(9-5)² + (a-1)² = (5-5)² + (a -5)² = r²
a² -2 a + 17 = a² - 10 a + 25 = r²
=> 8 a = 42
=> a = 21/4 = 5.25.
So r² = (a -5)² = 1/16
r = 1/4
So the circle area = π r² = π /16 sq units.