Question
The equation of an ellipse is $\mathrm{x}^{2} / \mathrm{a}^{2}+\mathrm{y}^{2} / \mathrm{b}^{2}=1$. Discuss what happens if $a=b=r$.
Step 1
If $a = b = r$, then the equation of the ellipse becomes: $\frac{x^2}{r^2} + \frac{y^2}{r^2} = 1$ Show more…
Show all steps
Your feedback will help us improve your experience
Nick Johnson and 93 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
You may have seen the equation for an ellipse as $\left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}=1$. What are $a$ and $b$ when the equation is written as $\lambda_{1} x^{2}+\lambda_{2} y^{2}=1 ?$ The ellipse $9 x^{2}+16 y^{2}=1$ has half-axes with lengths $a=$. and $b=$
Positive Definite Matrices
Tests for Positive Definiteness
Find parametric equations for the ellipse $$ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $$
Analytic Geometry
Plane Curves and Parametric Equations
Consider the ellipse whose equation is $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 .$ Show that if $a=b,$ then the graph is actually a circle.
Circles and Ellipses
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD