Tangent and normal to a hyperbola
Two-dimensional geometry · Mathematics
Study notes
Q: Find the tangent to x²/16 − y²/9 = 1 at (5, 9/4). (Check it's on: 25/16 − (81/16)/9 = 25/16 − 9/16 = 1 ✓.) Tangent: x(5)/16 − y(9/4)/9 = 1 → 5x/16 − y/4 = 1. Normal slope: tangent slope = 5/4, so normal slope = −4/5. Normal: y − 9/4 = (−4/5)(x − 5).