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f1refoxx
19.06.2021 •
Mathematics
Determine the equation of the circle graphed below.
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Ответ:
(x - 5)² + (y - 5)² = 18
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (5, 5) , then
(x - 5)² + (y - 5)² = r²
r is the distance from the centre to a point on the circle
Calculate r using the distance formula
r =![\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }](/tpl/images/1379/3962/05e0c.png)
with (x₁, y₁ ) = (5, 5) and (x₂, y₂ ) = (8, 8)
r =![\sqrt{(8-5)^2+(8-5)^2}](/tpl/images/1379/3962/1d9f1.png)
=![\sqrt{3^2+3^2}](/tpl/images/1379/3962/a5ae8.png)
=![\sqrt{9+9}](/tpl/images/1379/3962/99c0c.png)
=
⇒ r² = (
)² = 18
Then
(x - 5)² + (y - 5)² = 18 ← equation of circle
Ответ:
0.05, 0.2, 0.48, 0.6
Hope it helps