Tangent and normal to an ellipse
Two-dimensional geometry · Mathematics
Study notes
Q: Find the tangent and normal to x²/25 + y²/9 = 1 at (5·cosθ, 3·sinθ) for θ = π/3, i.e., point (2.5, (3√3)/2). Tangent: x(2.5)/25 + y(3√3/2)/9 = 1 → x/10 + y√3/6 = 1. Normal slope: perpendicular. Tangent slope m_t = −(b²x₁)/(a²y₁) = −(9×2.5)/(25×(3√3/2)) = −√3/5. Normal slope = 5/√3.