Question

select the correct answer. which point lies on the circle represented by the equation ((x + 7)^2 + (y - 10)^2 = 13^2)? a. ((5,12)) b. ((-7,-3)) c. ((-6,-10)) d. ((6,23))

Explanation:

Step1: Recall circle equation rule

A point $(x,y)$ lies on the circle $(x-h)^2+(y-k)^2=r^2$ if substituting $x,y$ satisfies the equation, where $13^2=169$.

Step2: Test Option A $(5,12)$

Substitute $x=5,y=12$:

$$(5+7)^2+(12-10)^2=12^2+2^2=144+4=148 eq169$$

Step3: Test Option B $(-7,-3)$

Substitute $x=-7,y=-3$:
$$(-7+7)^2+(-3-10)^2=0^2+(-13)^2=0+169=169$$

Step4: Verify remaining options (optional)

Test Option C $(-6,-10)$:

$$(-6+7)^2+(-10-10)^2=1^2+(-20)^2=1+400=401 eq169$$

Test Option D $(6,23)$:

$$(6+7)^2+(23-10)^2=13^2+13^2=169+169=338 eq169$$

Answer:

B. (-7,-3)