Question

Let L be a normal to the parabola y² = 4x. If L passes through the point (9, 6), then L is given by
(a) y – x + 3 = 0
(b) y + 3x – 33 = 0
(c) y + x – 15 = 0
(d) y – 2x + 12 = 0

Answer 1

Answer:

Step-by-step explanation:

BRAINLIEST BRAINLIEST BRAINLIEST

Answer 2

Option (b), y + 3x - 33 = 0 is correct.

Step-by-step explanation:

The given parabola is

y² = 4x

Differentiating both sides with respect to x, we get

2y dy/dx = 4

or, dy/dx = 2/y

Now dy/dx at the point (9, 6) = 2/6 = 1/3

So the slope of the normal is given by

m = (- dx/dy) at the point (9, 6)

= - 3

Using the point-slope formula, where the point is (9, 6) and the slope of the normal being (- 3), we get the required straight line as

y - 6 = (- 3) (x - 9)

or, y - 6 = - 3x + 27

or, y + 3x - 33 = 0

Thus option (b) is correct.