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The normal to the curve y(x-2)(x-3)=x+6 ...

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 : (1)`(1/2,-1/3)` (2) `(1/2,1/3)` (3) `(-1/2,-1/2)` (4) `(1/2,1/2)`

A

`(-(1)/(2), -(1)/(2))`

B

`((1)/(2), (1)/(2))`

C

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

D

`((1)/(2), (1)/(3))`

Text Solution

AI Generated Solution

To solve the problem, we need to find the normal to the curve \( y(x-2)(x-3) = x + 6 \) at the point where the curve intersects the y-axis. The steps are as follows: ### Step 1: Find the point of intersection with the y-axis The curve intersects the y-axis when \( x = 0 \). We can substitute \( x = 0 \) into the equation of the curve to find the corresponding \( y \) value. \[ y(0-2)(0-3) = 0 + 6 \] ...
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