a circle is centered at ( h(4, 0) ) and has a radius of 10.
where does the point ( l(-2, 8) ) lie?
choose 1 answer:
a inside the circle
b on the circle
c outside the circle

Question

Accepted Answer

# Explanation:
## Step1: Recall the distance formula
The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, the center of the circle $H(4,0)$ and the point $L(-2,8)$, so $x_1 = 4,y_1 = 0,x_2=-2,y_2 = 8$.
## Step2: Calculate the distance $HL$
Substitute the values into the distance formula:
$$
\begin{align*}
HL&=\sqrt{(-2 - 4)^2+(8 - 0)^2}\
&=\sqrt{(-6)^2+8^2}\
&=\sqrt{36 + 64}\
&=\sqrt{100}\
& = 10
\end{align*}
$$
## Step3: Compare with the radius
The radius of the circle is $10$. Since the distance between the center $H$ and the point $L$ is equal to the radius ($HL = 10=r$), the point $L$ lies on the circle.

# Answer:
B. On the circle

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the distance formula

Step2: Calculate the distance \(HL\)

Step3: Compare with the radius

Answer: