Bahan Ajar dan Bank Soal Matematika: Equation of Ellipse

Definition of Ellipse

Ellipse is the locus of points such that the distance of pairs of two different specific point is a certain constant. Two points given above is called the focal point

b² = a² - c²

General form of ellipse centered at O(0, 0) if the major axis parallel to the x axis :

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

General form of ellipse centered at O(0, 0) if the major axis parallel to the y axis :

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

Ellipse equation centered at P(α, β) if the major axis parallel to the x axis :

$\frac{\left (x-\alpha \right )^{2}}{a^{2}}+\frac{\left (y-\beta \right )^{2}}{b^{2}}=1$

Ellipse equation centered at P(α, β) if the major axis parallel to the y axis :

$\frac{\left (x-\alpha \right )^{2}}{b^{2}}+\frac{\left (y-\beta \right )^{2}}{a^{2}}=1$