Two Dimensional Analytical Geometry-II

A circle is the locus

A circle is the locus of all points equidistant from a fixed point (center). Standard form: (x-h)² + (y-k)² = r² with center (h,k) and radius r. Gener

A conic is the locus

A conic is the locus of a point P such that the ratio of its distance from a fixed point (focus) to a fixed line (directrix) is constant (eccentricity

A parabola (e=1) is the locus

A parabola (e=1) is the locus where distance to focus equals distance to directrix. Standard forms: y²=4ax (opens right), y²=-4ax (opens left), x²=4ay

An ellipse (0<e<1) has the property

An ellipse (0<e<1) has the property that sum of focal distances is constant (=2a). Standard form: x²/a² + y²/b² = 1 where a>b (major axis horizontal).

A hyperbola (e>1) has the property

A hyperbola (e>1) has the property that the absolute difference of focal distances is constant (=2a). Standard form: x²/a² - y²/b² = 1 (transverse axi