Which point lies on a circle with a radius of 5 units and center at P(6, 1)?
Q(1, 11), R(2, 4), S(4, -4), T(9, -2)
Solution:
An equation of circle is given by (x - a)2 + (y - b)2 = r2
Where a and b are coordinates of center, r is radius
Given, a = 6, b = 1 and r = 5
On substituting above values in equation of circle, we get,
(x - 6)2 + (y - 1)2 = 52
(x - 6)2 + (y - 1)2 = 25
From option (1),
Q(1, 11)
LHS = (x - 6)2 + (y - 1)2
= (1 - 6)2 + (11 - 1)2
= (- 5)2 + (10)2
= 25 + 100
= 125
RHS = 25
LHS ≠ RHS
From option 2,
R(2, 4)
LHS = (x - 6)2 + (y - 1)2
= (2 - 6)2 + (4 - 1)2
= (-4)2 + (3)2
= 16 + 9
= 25
RHS = 25
LHS = RHS
Therefore, the point R(2, 4) lies on the circle.
Which point lies on a circle with a radius of 5 units and center at P(6, 1)?
Summary:
For a circle with a radius of 5 units and center at P(6, 1), the point R(2 , 4) lies on the circle.
Math worksheets and
visual curriculum
visual curriculum
