Geometry of the Circle

x² + y² = r² (centre = (0,0) and radius = r)

(x - h)² +(y – k)² = r² (centre = (h,k) and radius =r)

x²+ y² + 2gx + 2fy +c = 0

(centre = (-g,-f) and 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.

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