If one end of a focal chord AB of the parabola y2 = 8x is at A \left(\right. \frac{1}{2} , - 2 \left.\right), then the equation of the tangent to it at B is :

Engineering

Mathematics

Tangent of Parabola

Question

If one end of a focal chord AB of the parabola y² = 8x is at $A (\frac{1}{2}, - 2)$ , then the equation of the tangent to it at B is :

2x - y - 24 = 0

2x + y - 24 = 0

x - 2y + 8 = 0

x + 2y + 8 = 0

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$Let (\frac{1}{2}, - 2) is (2 t^{2}, 4 t) \Rightarrow t = \frac{- 1}{2}$

Parameter of other end of focal chord is 2

⇒ point is (8, 8)

⇒ equation of tangent is 8y – 4(x+8) = 0

⇒ 2y – x = 8