Question

Write the following equation 5y2 − 4x2 = 20 in vertex form. Identify the type of conic section and its direction.

Answer 1

We will have te followinng:

*First: We remember the standard and vertex form for a quadratic function [In order]:

`y=ax^2+bx+c`

&

`y=a(x-h)^2+k`

*Second we solve the equation for y:

`5y^2-4x^2=20\Rightarrow5y^2=4x^2+20`
`\Rightarrow y=\pm\frac{2\sqrt[]{x^2+5}}{\sqrt[]{5}}`

So, from this we can infer that the equation is not in the vertex form, is an hyperbola with vertical openings. [As can be seen on the graph]:

**Equation in vertex form***

`y=\pm\frac{2\sqrt[]{x^2+5}}{\sqrt[]{5}}`