Question

Question #8d4f0

Answer 1

Please see below.

Explanation:

Form a
`sqrt(a-bx^2)` `" "`

Recall `1-sin^2theta = cos^2theta`

So turn `sqrt(a(1-b/ax^2))` into `sqrt(a(1-sin^2theta)`

using `sintheta = sqrt(b/a)x`

Form b
`sqrt(ax^2-b)` `" "`

Recall `sec^2theta - 1 = tan^2theta`

So turn `sqrt(a(b/ax^2-1))` into `sqrt(a(sec^2theta - 1)`

using `sectheta = sqrt(b/a)x`

Form c
`sqrt(a+bx^2)` `" "`

Recall `1+tan^2theta = sec^2theta`

So turn `sqrt(a(1+b/ax))` into `sqrt(a(1+tan^2theta)`

Don't forget to find `dx`!