Question

A circle with center C(4, -2) passes through the point A(1, 3). Does the point B(8, -2) lie inside the circle?

Answer 1

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1.A

2.D

3.A

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Answer 2

Answer:

Yes, point B will lie inside the circle.

Step-by-step explanation:          

Let the distance between point C and point A be the radius of our given circle.

We have been given that a circle with center C(4, -2) passes through the point A(1, 3).  

Since we know that a point will lie inside circle if the distance between the point and center of circle is less than radius of circle.

Let us find distance between points C and A using distance formula.

$\text{Radius}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

$\text{Radius}=\sqrt{(4-1)^{2}+(-2-3)^{2}}$

$\text{Radius}=\sqrt{(3)^{2}+(-5)^{2}}$

$\text{Radius}=\sqrt{9+25}$

$\text{Radius}=\sqrt{34}$

Radius of our circle is $\sqrt{34}$. Now let us find distance between center of our circle and point B.

$\text{Distance between C and B}=\sqrt{(4-8)^{2}+(-2--2)^{2}}$

$\text{Distance between C and B}=\sqrt{(-4)^{2}+(-2+2)^{2}}$

$\text{Distance between C and B}=\sqrt{16+(0)^{2}}$

$\text{Distance between C and B}=\sqrt{16}$

$\text{Distance between C and B}=4$    

We can see that distance of point B from center of our given circle is less than distance between point A and center of circle, therefore point B will lie inside the circle.