Question

A circle has its center at (6,-3). One point on the circle is (3, 1).
Which is another point that lies on the circle?

A. (10,-6)

B. (3,-5)

C. (-4, 10)

D. (4,-1)

Answer 1

Answer: A (10,-6)

Step-by-step explanation:

step 1:-  The equation of the circle is given center and radius is

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

Step 2:-

A circle has its center at (6,-3) and point on the circle is (3,1),Now

we have find radius from center to the given point on the circle

The distance of two points are

$\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1} )^2  }$

$\sqrt{(1-(-3))^2+(3-6)^2}$

$\sqrt{25}$

$r=5$

step 3:-

The equation of the circle having center and radius is

$(x-6)^{2}+(y+3)^2=5^{2}$

verification:

This circle is passing through the point (10,-6)

$(10-6)^{2}+(-6+3)^2=25$

$25 =25$

There fore the another point that lies on the circle is (10,-6).