SATHEE: Parabola 3 Question 6

Parabola 3 Question 6

6. Let $L$ be a normal to the parabola $y^{2} = 4 x$ . If $L$ passes through the point $(9, 6)$ , then $L$ is given by

(2011)

(a) $y - x + 3 = 0$

(b) $y + 3 x - 33 = 0$

(d) $y - 2 x + 12 = 0$

Show Answer

Answer:

Correct Answer: 6. $(a, b, d)$

Solution:

$m_{O P} = \frac{2 a t - 0}{a t^{2} - 0} = \frac{2}{t}$

$m_{O Q} = \frac{- 2 a / t}{a / t^{2}} = - 2 t$

$∴ \tan θ = \frac{\frac{2}{t} + 2 t}{1 - \frac{2}{t} \cdot 2 t} = \frac{2 t + \frac{1}{t}}{1 - 4} = \frac{- 2 \sqrt{5}}{3}$

where $t + \frac{1}{t} = \sqrt{5}$

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Parabola 3 Question 6

6. Let L be a normal to the parabola y2=4x. If L passes through the point (9,6), then L is given by

Answer:

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6. Let $L$ be a normal to the parabola $y^{2} = 4 x$ . If $L$ passes through the point $(9, 6)$ , then $L$ is given by