Question

Can you help me see if I'm doing this correctly

Answer 1

Given,

The center of the circle is (0,0).

The point on the circle is (6,8).

Required:

The radius of the circle and standard equation of the circle.

a)The radius of the circle is calculated as,

The radius of the circle is 10.

b)The standard equation of the circle is,

Hence, the equation of the circle is x^2+y^2=100.

c) The point on the third quadrant lies on the circle.

In the third quadrant both x and y values are negative.

So, the point lies in third quadrant is (-6, -8).

Hence, point on third quadrant is (-6, -8).

Answer 2

Given,

The center of the circle is (0,0).

The point on the circle is (6,8).

Required:

The radius of the circle and standard equation of the circle.

a)The radius of the circle is calculated as,

`\begin{gathered} Radius\text{ =}√((x_2-x_1)^2+(y_2-y_1)^2) \\ =√((6-0)^2+(8-0)^2) \\ =√(6^2+8^2) \\ =√(36+64) \\ =√(100) \\ =10 \end{gathered}`

The radius of the circle is 10.

b)The standard equation of the circle is,

`\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-0)^2+(y-0)^2=10^2 \\ x^2+y^2=100 \end{gathered}`

Hence, the equation of the circle is x^2+y^2=100.

c) The point on the third quadrant lies on the circle.

In the third quadrant both x and y values are negative.

So, the point lies in third quadrant is (-6, -8).

Hence, point on third quadrant is (-6, -8).