To calculate:The equation for the given circle which has points and . Also, its center is the midpoint of the given segment
The equation for the circle thathas points and , center is the midpoint of the given segment is
A circle withpoints and lying inside it and whose center is given by midpoint of
For a given circle with center and radius the equation is given as:
This is referred to as the Standard form for the equation of a given circle.
The Distance denoted by say, between any two given points say and is given as:
The midpoint for two points and is given as:
The relation between , diameter of circle and , radius of circle is:
Consider the given circle with points and lying inside it.
Then in order to apply the midpoint formula for the segment the following should be known:
Recall the midpoint for two points and is given as:
Hence, center of the circle is
Now as midpoint of forms the center of the circle, therefore length of gives the diameter for the circle.
And the relation between , diameter of circle and , radius of circle is:
Therefore, distance from center to gives the radius for the circle.
Recall the distance between two points and is given as:
As we have:
Also we have center
Recall that for a given circle with center and radius the equation is given as:
Therefore, replacing the values we get:
Now using the following formulae:
Then, reduces to:
Hence, the equation for the circle that has points and , center is the midpoint of the given segment is
Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!