Question

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

Answer 1

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Answer 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

→ dy/dx = [(x² - 5x + 6)(1)] - [(x + 6)(2x - 5)]/(x² - 5x + 6)².

At, x = 0 we have y = 1.

→ y = 6 - [(6)(-5)]/6² = 1

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)

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