Equation Of A Line

To find the equation of the normal to the curve at the point , we need to determine the slope of the tangent at the given point and then find the negative reciprocal to get the slope of the normal.

1. Derive the Curve: The derivative gives the slope of the tangent to the curve. For , the derivative is:

2. Evaluate at : Substitute to find the slope of the tangent at .

3. Slope of the Normal: The slope of the normal is the negative reciprocal of the tangent slope:

4. Equation of the Normal: Using the point-slope form of the line equation with point and slope , we have:

Simplifying, the equation is:

Or in standard form:

This matches the correct option, which is: x+2y=0.