# Question #6c148

##### 1 Answer

#### Answer:

The midpoint of the chord will start at one of the two points where the slope of the tangent line is equal to 1 and end at the other point where the slope of the tangent line is equal to 1.

#### Explanation:

Therefore, we need to find the two points on the ellipse where the slope of the tangent line is equal to 1.

Implicitly differentiate the given equation:

Set

Substitute

Substitute

The locus of the midpoint is a line segment between the points:

m =

The equation of the locus is the line segment: