Question

Select the correct answer.

Answer 1

Answer:

B.

Step-by-step explanation:

The general equation of a circle is $(x-h)^{2}+(y-k)^{2} = r^{2}$ where (h,k) is the center and r the radius. In this case, the general equation of the circle with radius 5 and center at (6,1) is $(x-6)^{2}+(y-1)^{2} = 5^{2}$, so the point that satisfies the equation will be in the circle.

A.  $(1-6)^{2}+(11-1)^{2} = 25+100 = 125$ this option is not correct.

B.   $(2-6)^{2}+(4-1)^{2} = 16+9= 25$ this option is correct so is the answer.

Answer 2

Answer:

Option B R(2,4) is correct

Step-by-step explanation:

The equation of the circle is:

$(x-a)^2 + (y-b)^2 = r^2$

Where r = radius

a and b are coordinates of the center of circle.

To check which point lies on a circle, we need to verify the equation

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

We will check for each option.

Option A Q(1,11)

x=1 and y =11

$(1-6)^2 + (11-1)^2 = 25\\(-5)^2 + (10)^2 = 25\\25 + 100 = 25\\125 \neq 25$

So, Option A is incorrect

Option B R(2,4)

x =2 and y = 4

$(2-6)^2 + (4-1)^2 = 25\\(-4)^2 + (3)^2 = 25\\16 + 9 = 25\\25 = 25$

Option B is correct.

Option C S(4,-4)

x =4 and y =-4

$(4-6)^2 + (-4-1)^2 = 25\\(-2)^2 + (-5)^2 = 25\\4 + 25 = 25\\29 \neq 25$

Option C is incorrect

Option D T(9,-2)

x =9 and y =-2

$(9-6)^2 + (-2-1)^2 = 25\\(3)^2 + (-3)^2 = 25\\9 + 9 = 25\\18 \neq 25$

Option D is incorrect.