Solve r=a*sec2θ

$$r = a \cdot \sec 2 \theta$$

Solve for a

$$a=r\cos(2\theta )$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{2}+\frac{\pi }{4}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$a\sec(2\theta )=r$$

The equation is in standard form.

$$\sec(2\theta )a=r$$

Divide both sides by \sec(2\theta ).

$$\frac{\sec(2\theta )a}{\sec(2\theta )}=\frac{r}{\sec(2\theta )}$$

Dividing by \sec(2\theta ) undoes the multiplication by \sec(2\theta ).

$$a=\frac{r}{\sec(2\theta )}$$

Divide r by \sec(2\theta ).

$$a=r\cos(2\theta )$$

Solve for r

$$r=\frac{a}{\cos(2\theta )}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\pi n_{1}}{2}+\frac{\pi }{4}$$