- #1

df606

- 14

- 0

## Homework Statement

Find a differential equation whose solution is a family of straight lines that are tangents to the circle [tex]x^2+y^2=a^2[/tex] where a is a constant.

## The Attempt at a Solution

So actually I'm stuck on the first part, coming up with such an equation. After some work I came up with

[tex]y=\pm(\frac{b(x+b)}{\sqrt{a^{2}-b^{2}}}+\sqrt{a^{2}-b^{2}})[/tex]

(b varies from -1 to 1 to produce the different straight lines)

which reduces to

[tex]y=\pm\frac{bx+a^{2}}{\sqrt{a^{2}-b^{2}}}[/tex]

and finding a differential equation whose solution is this family of straight lines is making my head hurt. Before I keep working I want to make sure this looks right. Graphing the equation works, but perhaps I'm misunderstanding the question.