Question

The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes through the point: 

(A) (1/2,  1/2)

(B) (1/2, - 1/3)

(C) (1/2, 1/3)

(D) (−1/2, - 1/2)

Answer 1

Answer is (A) (1/2, 1/2)

It is given that

y(x – 2)(x – 3) = x + 6

At y-axis, we know that x = 0. 

Therefore,

y(−2)(−3) = 0 + 6

Now, y(x² – 5x + 6) = x + 6

⇒ y = (x + 6)/(x² - 5x + 6)

Differentiating w.r.t. x, we get

Therefore, the equation of normal is

y – 1 = −1(x – 0)

That is, y + x  −1 = 0 or y + x = 1. 

Thus, the normal to the given curve line passes through (1/2, 1/2)