Question

Classify the following points as on the circle or not on the circle given by the equation (x + 1)² + (y - 3)2 = 6.25.

Answer 1

Substitute the points in the equation to check whether points lies on the circle or not.

$\begin{gathered} (0.5+\frac{1}{2})^2+(-3-3)^2=6.25 \\ 1+36=6.25 \\ 37\ne6.25 \end{gathered}$

Point (0.5,-3) lie not on the circle.

For point (1,1),

$\begin{gathered} (1+\frac{1}{2})^2+(1-3)^2=6.25 \\ 2.25+4=6.25 \\ 6.25=6.25 \end{gathered}$

Point (1,1) lie on the circle.

For point (-3,3),

$\begin{gathered} (-3+\frac{1}{2})^2+(3-3)^2=6.25 \\ (-2.5)^2+0=6.25 \\ 6.25=6.25 \end{gathered}$

Point (-3,3) lie on the circle.

For point (3,3),

$\begin{gathered} (3+\frac{1}{2})^2+(3-3)^2=6.25 \\ 12.25+0=6.25 \\ 12.25\ne6.25 \end{gathered}$

Point (3,3) lie not on the circle.

For point (-2,1);

$\begin{gathered} (-2+\frac{1}{2})^2+(1-3)^2=6.25 \\ (-1.5)^2+(-2)^2=6.25 \\ 2.25+4=6.25 \\ 6.25=6.25 \end{gathered}$

Point (-2,1) lie on the circle.