The tangent to the ellipse x²/a² + y²/b² = 1 at point (x₀, y₀):
x·x₀/a² + y·y₀/b² = 1
The tangent to the parabola y² = 4px at point (x₀, y₀):
y·y₀ = 2p(x + x₀)
Example ① Find the tangent to y² = 4x at point (1, 2).
Solution:2y = 2(x+1) → y = x + 1
Solution:2y = 2(x+1) → y = x + 1
Key Point
- For the tangent formula, replace “x²→x·x₀ and y²→y·y₀”
Practice Problems
- Find the tangent at point (√2, √2/2) on x²/4 + y² = 1.
Answers and Explanations
- Answer:x + 2y = 2√2
x·√2/4 + y·(√2/2) = 1。