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Question
The abscissa of the point on the curve 3y = 6x – 5x3, the normal at which passes through origin is ______.
Options
1
`1/3`
2
`1/2`
Solution
The abscissa of the point on the curve 3y = 6x – 5x3, the normal at which passes through origin is 1.
Explanation:
Let (x1, y1) be the point on the given curve 3y = 6x – 5x3 at which the normal passes through the origin.
Then we have `("dy"/"dx")_(x_1, y_1)`
= `2 - 5x_1^2`.
Again the equation of the normal at (x1, y1) passing through the origin gives `2 - 5x_1^2`
= `(-x_1)/y_1`
= `(-3)/(6 - 5x_1^2)`.
Since x1 = 1 satisfies the equation.
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