Sections:

# Graphing Ellipses

1) Horizontal Ellipse: $$\frac{x^2}{a^2}+ \frac{y^2}{b^2}=1$$ 2) Vertical Ellipse: $$\frac{x^2}{b^2}+ \frac{y^2}{a^2}=1$$ To graph an equation of this format, we plot the x-intercepts and the y-intercepts. We can find the x-values by taking the positive and negative square roots of the denominator under x-squared. We can find the y-values by taking the positive and negative square roots of the denominator under y-squared. We then draw a smooth curve through the four points. A more challenging scenario occurs when we see an ellipse that is shifted horizontally or vertically. As an example, suppose we see the equation: $$\frac{(x-3)^2}{25}+ \frac{(y+2)^2}{9}=1$$ Here the center has shifted to (3, -2) and so all of our points have shifted 3 units right and 2 units down.