# General Equa ons of a Hyperbola ```CONIC SECTIONS SPECIFIC OBJECTIVES: At the end of the lesson, the student is expected to be able to: • give the proper9es of hyperbola. • write the standard and general equa9on of a hyperbola. • sketch the graph of hyperbola accurately. THE HYPERBOLA (e &gt; 1) A hyperbola is the set of points in a plane such that the diﬀerence of the distances of each point of the set from two ﬁxed points (foci) in the plane is constant. The equa9ons of hyperbolas resemble those of ellipses but the proper9es of these two kinds of conics diﬀer considerably in some respects. To derive the equa9on of a hyperbola, we take the origin midway between the foci and a coordinate axis on the line through the foci. The following terms are important in drawing the graph of a hyperbola; Transverse axis is a line segment joining the two ver9ces of the hyperbola. Conjugate axis is the perpendicular bisector of the transverse axis. General EquaGons of a Hyperbola 1. Horizontal Transverse Axis : Ax2 – Cy2 + Dx + Ey + F = 0 2. VerGcal Transverse Axis: Cy2 – Ax2 + Dx + Ey + F = 0 HYPERBOLA WITH CENTER AT THE ORIGIN C(0,0) Then leIng b2 = c2 – a2 and dividing by a2b2, we have if foci are on the x-&shy;‐axis if foci are on the y-&shy;‐axis The generalized equa9ons of hyperbolas with axes parallel to the coordinate axes and center at (h, k) are if foci are on a axis parallel