Which point is on the circle centered at the origin with a radius of 5 units?
(2, √21), (2, √23), (2, 1), (2, 3)

Solution:

An equation of circle is given by

(x - a)² + (y - b)² = r²

Where a and b are coordinates of center and

r is radius

Given, a = 0, b = 0 and r = 5

On substituting above values in equation of circle, we get,

(x - 0)² + (y - 0)² = 5²

x² + y² = 25

(i) From option(1), (2, √21)

LHS = (2 - 0)² + (√21 - 0 )²

= 4 + 21

= 25

RHS = 25

LHS = RHS

(ii) From option(2), R(2 , 1)

LHS = (2 - 0)² + (1 - 0)²

= 4 + 1

= 5

RHS = 25

LHS ≠ RHS

(iii) From option(3)LHS = (2 - 0)² + (1 - 0 )²

= 4 + 1

= 5

RHS = 25

LHS ≠ RHS

(iv)From option(4) LHS = (2 - 0)² + (3- 0 )²

= 4 + 9

= 13

RHS = 25

LHS ≠ RHS

Therefore, the points R(2, √21) lies on the circle.

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Which point is on the circle centered at the origin with a radius of 5 units?

Summary:

The point on the circle centered at the origin with a radius of 5 units is (2 , √21).