Answer :
Answer: [tex](x-5)^2+(y+4)^2=10^2[/tex]
Step-by-step explanation:
The standard of equation of a circumference has the form:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
Where the point (a,b) is the center of the circumference and r is the radius.
You know the center of the circumference: (5,-4).
Substitute this point into the equation of the circumference:
a=5 and b=-4
Then:
[tex](x-5)^2+(y+4)^2=r^2[/tex]
Now you need to find the radius. Substitute the point (-3,2) into the circumference and solve for r:
[tex](-3-5)^2+(2+4)^2=r^2\\(-8)^2+(6)^2=r^2\\64+36=r^2\\r=\sqrt{100}\\r=10[/tex]
The equation of this circumference is:
[tex](x-5)^2+(y+4)^2=10^2[/tex]
Answer:
[tex](x-5)^2+(y+4)^2=100[/tex]
Or type
(x + _-5__)^2 + (y + _4__)^2 = _100__.
Step-by-step explanation:
First find the radius of the circle using the distance formula;
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute the points to get;
[tex]r=\sqrt{(5--3)^2+(-4-2)^2}[/tex]
[tex]r=\sqrt{8^2+(-6)^2}[/tex]
[tex]r=\sqrt{64+36}[/tex]
[tex]r=\sqrt{100}[/tex]
r=10 units
We now substitute the center (h,k)=(5,-4) and r=10 into the standard equation of the circle;
[tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](x-5)^2+(y--4)^2=10^2[/tex]
[tex](x-5)^2+(y+4)^2=100[/tex]