simonjordan2008
New member
- Joined
- Nov 5, 2007
- Messages
- 8
Consider the rectangular hyperbola xy = c2 with parametrization (x, y) = (ct, c/t), and t not equal to 0.
1. Derive (i.e. do not just quote) the equations of the tangent and normal at the point P with (parametric) coordinates (cp, c/p).
2. Consider the points P : (cp, c/p) and Q : (cq, c/q) on the hyperbola. Find the equation of the straight line that joins the points P and Q.
3. Consider a point R : (cr, c/r) also on the hyperbola, and suppose that in the triangle PRQ, \PRQ = 90◦. Prove that the normal (to the hyperbola) at R is parallel to the line PQ.
1. Derive (i.e. do not just quote) the equations of the tangent and normal at the point P with (parametric) coordinates (cp, c/p).
2. Consider the points P : (cp, c/p) and Q : (cq, c/q) on the hyperbola. Find the equation of the straight line that joins the points P and Q.
3. Consider a point R : (cr, c/r) also on the hyperbola, and suppose that in the triangle PRQ, \PRQ = 90◦. Prove that the normal (to the hyperbola) at R is parallel to the line PQ.