SME
Grade 10 Math · Geometry
Equations of circles
Use this for “Write the equation of the circle with center (3, −2) and radius 5.”
Diagram
(x − 3)² + (y + 2)² = 25
Center (3, −2)
radius 5.
This is an example. Type your own values to start a new problem.
(x
−
h
)²
+
(y
−
(
k
)
)²
=
q
A center below or left of 0 is typed with its minus: (y + 2)² is (y − (−2))², so k is −2.
r
Radius
example
Formulas
q
=
r
2
25
=
5
2
Assumptions
•
Every point (x, y) on the circle is r from the center (h, k).
•
The distance formula squared gives (x − h)² + (y − k)² = r².
•
A center with a negative coordinate turns the minus into a plus: (y + 2)² has k = −2.
Step-by-step
WE KNOW
h = 3, k = −2, r = 5
FIND
right side, r² (q)
Step 1 · Find right side, r² (q)
Use q = r²
Square the radius for the right side.
q
=
5
2
q
=
25
so
(x − 3)
2
+
(y + 2)
2
=
25
Check
Put the numbers back in. Both sides should match.
25
=
5
2
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
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