Question

Can anyone help me with these question

Answer 1

So hmm notice the picture below

a)

the center of the circle is the midpoint of those two folks

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -10}}\quad ,&{{ -2}})\quad % (c,d) &({{ 4}}\quad ,&{{ 6}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left(\cfrac{4-10}{2}\quad ,\quad \cfrac{6-2}{2} \right)\impliedby \textit{center of the circle}$

b)

the diameter is the distance between P and Q, or the length  of that segment, and the radius is half the diameter

$\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -10}}\quad ,&{{ -2}})\quad % (c,d) &({{ 4}}\quad ,&{{ 6}}) \end{array}\quad % distance value d = \sqrt{({{ 4}}-{{ (-10)}})^2 + ({{ 6}}-{{ (-2)}})^2} \\\\\\ d=\cfrac{\sqrt{(4+10)^2+(6+2)^2}}{2}\impliedby \textit{radius of the circle}$

c)

so, from a), you found the h,k coordinates for the center, from b) you've got the radius

so, just plug them in here then $\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{ k}})\qquad radius=&{{ r}} \end{array}$