Sketch the graph of the ellipse \(\ds \frac{x^2}{9}+\frac{y^2}{16}=1\) and determine its foci. Let \(C\) be the conic which consists of all points \(P=(x,y)\) such ...

Learn all about parabolas in conic sections. We will discover the basic definitions such as the vertex, focus, directrix, and ...

(a) \(\ds e=\frac{1}{2}\text{.}\) (b) Use the fact that, for \(P=(x,y)\text{,}\) \(\ds |PF|^2=x^2+(y-1)^2\) and \(\ds |Pl|=\frac{1}{2}|y-4|\text{.}\) (c) From \(\ds ...

THE question of the true geometric interpretation of the Mongian equation has been often considered by mathematicians. In the first place, we have the late Dr. Boole's statement that “here our powers ...

A multifocal metalens, which focuses incident light at multiple foci, has many applications in imaging systems and optical communications. However, the traditional design strategy of a multifocal ...