Circles

A circle is the locus

A circle is the locus of points at constant distance (radius 'r') from a fixed point (centre). Standard form: (x-h)² + (y-k)² = r² where (h,k) is cent

x² + y² + 2gx +

x² + y² + 2gx + 2fy + c = 0 represents a circle with centre (-g,-f) and radius √(g²+f²-c). Conditions: coefficients of x² and y² are equal, no xy term

Circle with centre (h

Circle with centre (h,k) and radius r: x = h + r cos θ, y = k + r sin θ where θ is parameter. For unit circle at origin: x = cos θ, y = sin θ. This fo

For circle S = x² +

For circle S = x² + y² + 2gx + 2fy + c = 0 and point P(x₁,y₁): S₁₁ < 0 (inside), S₁₁ = 0 (on circle), S₁₁ > 0 (outside). Power of point = S₁₁. Length

Tangent at point (x₁

Tangent at point (x₁,y₁) on circle S = 0: equation is S₁ = 0. Normal passes through centre and point of tangency. For x² + y² = r², tangent at (x₁,y₁)