The equation of the circle is 2x²+4x+2y²+4y-21=0.
The given points are P= (-4,-3) and Q= (2,1).
We need to find the equation of the circle.
What is the equation of the circle?
The formula for the equation of a circle is (x – h)²+ (y – k)² = r², where (h, k) represents the coordinates of the centre of the circle, and r represents the radius of the circle.
Using the distance formula and finding the diameter, that is [tex]\sqrt{(2+4)^{2}+(1+3)^{2} }[/tex]
=√50=5√2 units
Radius=5/√2
Using the midpoint formula we can find the centre. Since ends of diameter are given.
That is, x=[(-4+2)/2]=-1 and y=[(-3+1)/2]=-1
So, the centre of the circle is (-1, -1).
Then, equation is (x +1)²+ (y +1)² = (5/√2)²
⇒x²+2x+1+y²+2y+1=25/2
⇒2x²+4x+2y²+4y=21
⇒2x²+4x+2y²+4y-21=0
Therefore, the equation of the circle is 2x²+4x+2y²+4y-21=0.
To learn more about the circle equation visit:
https://brainly.com/question/10618691.
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