2. Equation of a Circle Theorem
• The locus of a point is a circle with centre
(h,k) and radius r.
• In standard form the equation is:
(x-h)2 + (y-k)2 = r2
• If the circle is centred
on the origin, then
x2 + y2 = r2
3. General Form
• In the general form, the equation of a
circle is:
• Ax2 + Bxy + Cy2 + Dx + Ey +F = 0
• D = -2h
• E = -2k
• F = h2 + k2 - r2
• Put this on your review sheet definitely!
5. Inequalities
• Inequalities with circles are E-Z.
• (x-h)2 + (y-k)2 < r2 occurs on the
INSIDE of a circle with a dashed
circumference.
• (x-h)2 + (y-k)2 ≥ r2 occurs on the
OUTSIDE of a circle with a solid line.
The solution set includes the line.
6. Of Note…
• The centre (h,k) occurs at the midpoint of
the diameter.
• A tangent touches a circle at one point
only AND at 90º to the radius of the circle.
7. Exam Question
• What is the equation of the tangent to the
circle with the equation
(x 3)2 + (y 1)2 = 5 which passes
through the point (2, -1)?
• A) 2x + y = 0
• B) 2x y = 0
• C) x + 2y = 0
• D) x 2y = 0
