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Identify the point on the curve 9y² = x³ where the normal to the curve intersects the coordinate axes at equal distances.

1. (4, 8/3)
2. (-4, 8/3)
3. (4, -8/3)
4. None of these

Correct answer: (4, 8/3)

Solution

To find the point where the normal intersects the axes at equal distances, we need to find where the slope of the tangent is equal to the negative reciprocal of the slope of the normal, which is satisfied at the point (4, 8/3).

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