Question

a circle is centered at m(0, 0). the point b(-4, √5) is on the circle. where does the point a(5, -1) lie? choose 1 answer: a inside the circle b on the circle c outside the circle

Explanation:

Step1: Calculate the radius of the circle

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For the center of the circle $M(0,0)$ and point $B(-4,\sqrt{5})$, the radius $r$ of the circle is the distance between $M$ and $B$. So $r=\sqrt{(-4 - 0)^2+(\sqrt{5}-0)^2}=\sqrt{16 + 5}=\sqrt{21}$.

Step2: Calculate the distance between the center and point $A$

For the center $M(0,0)$ and point $A(5,-1)$, the distance $d_{MA}=\sqrt{(5 - 0)^2+(-1 - 0)^2}=\sqrt{25+1}=\sqrt{26}$.

Step3: Compare the distance and the radius

Since $\sqrt{26}>\sqrt{21}$ (because if $a>b>0$, then $\sqrt{a}>\sqrt{b}$), the distance from point $A$ to the center of the circle is greater than the radius of the circle.

Answer:

C. Outside the circle