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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 \(\mathsf{(1,\,-2):}\)
\(\mathsf{1^2+(-2)^2}\\\\ \mathsf{1+4}\\\\ \mathsf{5
e 25\qquad\quad\diagup\hspace{-9}\diagdown}\)
The point \(\mathsf{(1,\,-2)}\) doesn't lie in the circumference.
• Testing \(\mathsf{(\sqrt{5},\,\sqrt{5}):}\)
\(\mathsf{(\sqrt{5})^2+(\sqrt{5})^2}\\\\ \mathsf{5+5}\\\\ \mathsf{10
e 25\qquad\quad\diagup\hspace{-9}\diagdown}\)
So, the point \(\mathsf{(\sqrt{5},\,\sqrt{5})}\) doesn't lie in the circumference either.
Answer: (–3, 4).
I hope this helps. =)
