Question

The circle has center N and radius MN has equation what?M (-2,1) and N(2,4)

Answer 1

`(x-2)^2+(y-4)^2=25`

Step-by-step explanation:

Given a circle with center N(2,4) and radius MN where M(-2,1).

First, we find the length of the radius using the distance formula.

`\begin{gathered} MN=\sqrt[]{(-2-2_{})^2+(1-4)^2} \\ =\sqrt[]{(4_{})^2+(-3)^2} \\ =\sqrt[]{25} \\ r=5\text{ units} \end{gathered}`

The equation of a circle is of the form:

`(x-h)^2+(y-k)^2=r^2`

(h,k)=N(2,4), r=5

Therefore, the equation is:

`\begin{gathered} (x-2)^2+(y-4)^2=5^2 \\ (x-2)^2+(y-4)^2=25 \end{gathered}`