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Select the correct answer. Which point lies on a circle with a radius of 5 units and center at P(6, 1)? A. Q(1, 11) B. R(2, 4) C. S(4, -4) D. T(9, -2)

2 Answers

7 votes

Answer:

T(9,-2)

Explanation:

The circle has radius 5 units and center P(6,1).

The equation of this circle is


(x-6)^2+(y-1)^2=5^2


(x-6)^2+(y-1)^2=25

If Q(1,11) lies on this circle, then it must satisfy its equation.


(1-6)^2+(11-1)^2=25


(-5)^2+(10)^2=25


25+100=25, this statement is false.

If R(2,4) lies on this circle, then it must satisfy its equation.


(2-6)^2+(4-1)^2=25


(-4)^2+(3)^2=25


16+9=25, this statement is false.

If S(4,-4) lies on this circle, then it must satisfy its equation.


(4-6)^2+(-4-1)^2=25


(-2)^2+(-5)^2=25


4+25=25, this statement is false.

If T(9,-2) lies on this circle, then it must satisfy its equation.


(9-6)^2+(-2-1)^2=25


(4)^2+(-3)^2=25


16+9=25, this statement is TRUE.

The correct answer is D

User Rudimeier
by
8.4k points
3 votes

Answer:

Option B)

R(2,4)

Explanation:

Given that P(6,1) is the center of the circle.

Let us find each point distance from P if equal to 5 units, then the point lies on the circle

PQ =
√((1-6)^2+(11-1)^2) =√(125) \\=5√(3)

PR =
√((2-6)^2+(4-1)^2) =√(25) =5

PS =
√((4-6)^2+(-4-1)^2) \\=√(29)

PT =
√((9-6)^2+(-2-1)^2) \\=√(18) \\=3√(2)

We see that only R is having a distance of 5 units from P.

Hence R lies on the circle

Option B)

R(2,4)

User One Monkey
by
8.1k points

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