Question

Which point lies on the circumference of a circle with center (6,5) that passes through the point (9,8)? A. (3,2) B. (4,7) C. (6,2) or D. (12,11)

Answer 1

Answer:

A. (3,2)

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance between the center of the circle and any point on the circumference is equal to the radius of the circle

we have the ordered pairs

(6,5) and (9,8)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute

$r=\sqrt{(8-5)^{2}+(9-6)^{2}}$

$r=\sqrt{(3)^{2}+(3)^{2}}$

$r=\sqrt18}\ units$

step 2

Find the equation of the circle

$(x-h)^2+(y-k)^2=r^2$

substitute the given values

$(x-6)^2+(y-5)^2=(\sqrt18})^2$

$(x-6)^2+(y-5)^2=18$

step 3

Verify each ordered pair

Remember that

If a ordered pair lie on the circumference of the circle, then the ordered pair must satisfy the equation of the circle

A) we have

(3,2)

substitute the value of x and the value of y in the equation of the circle

$(3-6)^2+(2-5)^2=18$

$(-3)^2+(-3)^2=18$

$18=18$ ----> is true

so

The ordered pair lie on the circumference of the circle

B) we have

(4,7)

substitute the value of x and the value of y in the equation of the circle

$(4-6)^2+(7-5)^2=18$

$(-2)^2+(2)^2=18$

$8=18$ ----> is not true

so

The ordered pair not lie on the circumference of the circle

C) we have

(6,2)

substitute the value of x and the value of y in the equation of the circle

$(6-6)^2+(2-5)^2=18$

$(0)^2+(-3)^2=18$

$9=18$ ----> is not true

so

The ordered pair not lie on the circumference of the circle

D) we have

(12,11)

substitute the value of x and the value of y in the equation of the circle

$(12-6)^2+(11-5)^2=18$

$(6)^2+(6)^2=18$

$72=18$ ----> is not true

so

The ordered pair not lie on the circumference of the circle