Question

The diameter of Circle Q terminates on the circumference of the circle at (3,0) and (-4,0). Write the equation of the circle in standard form. Show all of your work for full credit.

Answer 1

Answer: $(x+0.5)^2+y^2=49$

Step-by-step explanation:

Given

The diameter of circle terminates on the circumference with coordinates

(3,0) and (-4,0)

Distance between the two points is the diameter of the circle. The distance is given by distance formula i.e. $d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

Insert the values

$\Rightarrow d=\sqrt{\left(-4-3\right)^2+\left(0-0\right)^2}\\\\\Rightarrow d=\sqrt{(-7)^2+0}\\\Rightarrow d=7\\\text{So, the radius is r=}3.5\ \text{units}$

The center of the circle is the mid-point of the two points i.e.

$\Rightarrow x=\dfrac{3-4}{2}\\\\\Rightarrow x=-\dfrac{1}{2}\\\\\Rightarrow y=\dfrac{0+0}{2}\\\\\Rightarrow y=0\\\Rightarrow (x,y)\rightarrow (-\dfrac{1}{2},0)$

The equation of the circle is given by

$\Rightarrow (x-(0.5))^2+(y-0)^2=7^2\\\\\Rightarrow (x+0.5)^2+y^2=49$