Question

Center: (15, 2) Point on Circle: (19,2)

Answer 1

SOLUTION

FORMULA ; Equation of a circle

$(x-a)^2+(y-b)^2=r^2$

(a,b)= coordinates of the centre

r= radius

The radius is the distance from the point on the circle to the centre

The distance can be obtained as shown

$\begin{gathered} radius=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ x_1=15 \\ x_2=19 \\ y_1=2 \\ y_2=2 \\ radius=\sqrt{(2-2)^2+(19-15)^2} \\ radius=\sqrt{16}=4 \end{gathered}$

Now the equation of the circle

$\begin{gathered} (x-15)^2+(y-2)^2=4^2 \\ (x-15)^2+(y-2)^2=16 \end{gathered}$$\begin{gathered} x^2-30x+225+y^2-4y+4=16 \\ x^2+y2-30x-4y+225+4-16=0 \\ x^2+y^2-30x-4y+213=0 \end{gathered}$