Circles

The standard form of the equation

The standard form of the equation of a circle with centre (h, k) and radius r is (x - h)² + (y - k)² = r². This form directly shows the centre and rad

The general second

The general second-degree equation x² + y² + 2gx + 2fy + c = 0 represents a circle if it satisfies certain conditions. The centre is (-g, -f) and the

If the endpoints of a diameter

If the endpoints of a diameter are (x₁, y₁) and (x₂, y₂), then the equation of the circle is (x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0. This is derived

The tangent to a circle at

The tangent to a circle at a point P(x₁, y₁) is the line that touches the circle only at that point. Its equation is S₁ = 0, where S is the circle's e

Two circles are said to be

Two circles are said to be orthogonal if they intersect at right angles. The condition for orthogonality of circles x² + y² + 2gx + 2fy + c = 0 and x²