Hyperbola 4Given the two foci (F1 and F2) and a line tangent to the curve, construct the hyperbola and the point of tangency.  The given foci must fall on opposite sides of the tangent line. Reflect point F1 across the tangent line, and let its image be F1ʹ. Line F2F1ʹ intersects the tangent line at the point of tangency.  The figure now has the two foci and one other point on curve. Complete the construction using Hyperbola 3 as a guide. The websketch below has the completed construction. Drag the given objects to confirm it. |