Question

Use the information provided to write the general conic form equation of the circle: Ends of a diameter: (11, -2) and (9, 4)

Answer 1

The equation for a circle is:

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

Where (a,b) is the circle's center and r is the circle's radius.

First, we can find the center point of the circle. Because the two points from the problem are the endpoints of a diameter, the midpoint of the line segment is the center point of the circle.

The formula to find the mid-point of a line segment giving the two endpoints is:

M = $(\frac{x_{1} + x_{2} }{2}$, $\frac{y_{1} + y_{2} }{y} )$

Where M is the midpoint and the given points are:

$(x_{1}, y_{1} )$ and $(x_{2} , y_{2})$

Substituting the values from the two points in the problem gives:

$M = (\frac{11+9}{2}$,$\frac{-2+4}{2} )$

$M = (\frac{11+9}{2}$,$\frac{2-4}{2})$

$M = (\frac{20}{2} , \frac{2}{2})$

$M = (10,1)$