Question

a circle has a center at (1,-2) and a radius of 4. does the point (3.4,1.2) lie on the circle? justify your answer

Answer 1

`\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{ k}})\qquad radius=&{{ r}}\\ &\uparrow &\uparrow &\uparrow \\ &1&-2&4 \end{array} \\\\\\ (x-1)+(y-(-2))=4^2\implies (x-1)+(y+2)=4^2\\\\ -----------------------------\\\\ \begin{cases} x=3.4\\ y=1.2 \end{cases}\implies (3.4-1)+(1.2+2)=4^2`

so hmm does the left-hand-side give you 16?

if it does, then the equation is true, and that point does lie on the circle