Find the equation for the circle with a diameter whose endpoints are (3,-1) and (-2,-1)

The equation for the circle is:

Step-by-step explanation:

Here, let us assume the two end points of the diameter are:

P (3,-1) and Q (-2,-1)

Now, as we knew diameter is the chord that passer through the center of the circle.

⇒ Mid point of DIAMETER  = Center coordinates  of the Circle

Let us assume O(x,y) is the center of the line  segment PQ.

So, by MID POINT FORMULA:

⇒ The center coordinates of the circle  = O(0.5,-1)   ...... (1)

Now, RADIUS = Half of DIAMETER

Using DISTANCE FORMULA:

So, Radius  = 5/2  = 2.5 units

Now, the  equation of circle with radius r and center coordinate ( h,k) is given as:

Substitute r = 2.5 and (h,k)  = (0.5,0) we get:

Hence the equation for the circle is:

the answer

b. they are parallel and will never intersect.

correct answers below: