Question

Which of the following points lies on the circle whose center is at the origin and whose radius is 5?

(-3, 4)
(1, -2)
(√5,√5)

Answer 1

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Equation of the circumference whose center is at $\mathsf{C(0,\,0)}$ and whose radius is $\mathsf{r=5:}$

$\mathsf{(x-x_C)^2+(y-y_C)^2=r^2}\\\\ \mathsf{(x-0)^2+(y-0)^2=5^2}\\\\ \mathsf{x^2+y^2=25}$


We are looking for the point that satisfies the equation above.


•  Testing $\mathsf{(-3,\,4):}$

$\mathsf{(-3)^2+4^2}\\\\ \mathsf{9+16}\\\\ \mathsf{25\qquad\quad\checkmark}$


The point $\mathsf{(-3,\,4)}$ lies in the circumference.


•  Testing $\mathsf{(1,\,-2):}$

$\mathsf{1^2+(-2)^2}\\\\ \mathsf{1+4}\\\\ \mathsf{5\ne 25\qquad\quad\diagup\hspace{-9}\diagdown}$


The point $\mathsf{(1,\,-2)}$ doesn't lie in the circumference.


•  Testing $\mathsf{(\sqrt{5},\,\sqrt{5}):}$

$\mathsf{(\sqrt{5})^2+(\sqrt{5})^2}\\\\ \mathsf{5+5}\\\\ \mathsf{10\ne 25\qquad\quad\diagup\hspace{-9}\diagdown}$


So, the point $\mathsf{(\sqrt{5},\,\sqrt{5})}$ doesn't lie in the circumference either.



Answer:  (–3,  4).


I hope this helps. =)

Answer 2

Answer:

(-3,4)

Step-by-step explanation:

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