Which point does not lie on the circle centered at (3, 2) with radius 5?
A(0,6), B(3,-3), C(-2,2), D(3,0)

Solution:

Given, centre of the circle (h, k) = (3, 2)

Radius of the circle, r = 5

We have to find the point that does not lie on the circle.

The general form of the equation of the circle with centre (h, k) and radius r is given by

(x - h)2 + (y - k)2 = r2

r2 = (5)2 = 25

From the options,

A(0, 6)

LHS: (x - h)2 + (y - k)2

(x - h)2 = (0 - 3)2 = 32 = 9

(y - k)2 = (6 - 2)2 = 42 = 16

(x - h)2 + (y - k)2 = 9 + 16 = 25

RHS: r2 = 25

LHS = RHS.

Therefore, the point (0, 6) lies on the circle.

B(3, -3)

LHS: (x - h)2 + (y - k)2

(x - h)2 = (3 - 3)2 = 0

(y - k)2 = (-3 - 2)2 = (-5)2 = 25

(x - h)2 + (y - k)2 = 0 + 25 = 25

RHS: r2 = 25

LHS = RHS.

Therefore, the point (3, -3) lies on the circle.

C(-2, 2)

LHS: (x - h)2 + (y - k)2

(x - h)2 = (-2 - 3)2 = (-5)2 = 25

(y - k)2 = (2 - 2)2 = 0

(x - h)2 + (y - k)2 = 0 + 25 = 25

RHS: r2 = 25

LHS = RHS.

Therefore, the point (-2, 2) lies on the circle.

D(3, 0)

LHS: (x - h)2 + (y - k)2

(x - h)2 = (3 - 3)2 = 0

(y - k)2 = (0 - 2)2 = (-2)2 = 4

(x - h)2 + (y - k)2 = 0 + 4 = 4

RHS: r2 = 25

LHS ≠ RHS.

Therefore, the point (3, 0) does not lie on the circle.

Therefore, (3, 0) does not lie on the circle.

Which point does not lie on the circle centered at (3, 2) with radius 5?

Summary:

The point (3, 0) does not lie on the circle centered at (3, 2) with radius 5.

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