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

Engineering

Mathematics

Normal to Parabola

Question

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

y + 3x – 33 = 0

y + x – 15 = 0

y – x + 3 = 0

y – 2x + 12 = 0

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y = mx – 2m – m³

It passes through (9, 6)

6 = 9m –2m – 2m – m³

m³ – 7m 6 = 0

(m – 1) (m – 2) (m + 3) = 0

$∴$ m = –3, 1, 2

Hence equation will be

y = x – 3, y = 2x – 12 and y = –3x + 33