Question

Which point does not lie on the circle with center (0,0) and radius 10? A. (6,8) B. (0, 10) C. (10,-8) O D. (-8, 6)

Answer 1

C. (10, -8)

Step-by-step explanation:

The equation of a circle is given as:

`\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{Centre}=(h,k) \\ \text{Radius}=r \end{gathered}`

Given a circle with centre (0,0) and radius 10, its equation is:

`\begin{gathered} x^2+y^2=10^2 \\ x^2+y^2=100\ldots(1) \end{gathered}`

To determine the point that does not lie on the circle, we check the point that does not satisfy the equation (1) derived above:

• Point (6,8)

`\begin{gathered} x=6,y=8 \\ 6^2+8^2=100 \\ 36+64=100 \\ 100=100 \end{gathered}`

• Point (0,10)

,

•

• Point (10, -8)

`\begin{gathered} x=10,y=-8 \\ 10^2+(-8)^2=100 \\ 100+64=100 \\ 164\\eq100 \end{gathered}`

It is clear that point (10,-8) does not lie on the circle since the outcome is False.

The correct choice is C.