If the line is normal to the curve , then:
Explanation for the correct options:
Normal on the curve:
Given curve is
So,
Differentiating with respect to , we get,
Given line is,
The slope of a line is the coefficient of in form.
Thus, the slope of the given line is,
Thus the slope of tangent is,
Since the slope is normal to the curve, the normal of the line will be tangent to the curve. Thus,
So, will always be a positive value, so in the must be negative. For that to happen, and must have the opposite signs.
Thus, or .
Therefore, option A is correct.