MATHS PAPER 2 NOTES
Circle
x² + y² = r²
(x - h)² +(y – k)² = r²
for a circle x² + 2gx + 2fy + y²
centre = (-g,-f)
radius= √ g²
+f² -c if √ g² +f² -c >0 and the coefficients of x² and
y² are 1
If two circles touch externally the distance between the
centres equals the sum of their radii.
If two circles touch internally the distance
between their centres equals the difference between their radii.
For a circle with centre (0,0) intersecting a point
(x₁,y₁)
x₁x
+ y₁y
= r²
For a circle with centre (-g, -f)
intersecting a point (x₁,y₁)
x ₁x +
y₁
y g(x
+ x ₁)
+f(y +
y ₁)
+ c = 0
S₁
- S₂ =
0 is the equation for the common chord between two circles S₁
and S₂
x=rcosθ and y =rsinθ are parametric equations of
a circle with centre (0,0) and radius r.