Chord with Given Midpoint

Chord with Given Midpoint

For a central conic, the chord whose midpoint is $$M(x_1,y_1)$$ can be obtained using the diameter relation.

For the ellipse:

$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$

the diameter corresponding to a family of parallel chords has equation:

$$\frac{x x_1}{a^2}+\frac{y y_1}{b^2}=1$$

Usage

- Used in problems involving the midpoint of a chord and its associated diameter.