Solving intercept from an equation

Question

I am confused to solve (a) in this equation.

$$y=x^2/(a+bx)^2$$

What I got is:

$$a=(x-bx)/(sqrt(y)).$$

Is that right or not because when I use this equation by substituting numbers of the variables I couldn't get my desired result.

Thanks in advance

Answer 1

You can solve for $a$ step-by-step as follows:

$$y = \frac{x^2}{(a+bx)^2} \iff (a+bx)^2 = \frac{x^2}{y}$$

$$\implies a+bx = \pm{\sqrt{\frac{x^2}{y}} = \pm\color{green}{\frac{x}{\sqrt{y}}}} = \pm\color{blue}{\frac{x\sqrt{y}}{y}}$$

$$\implies a = \pm\color{green}{\frac{x}{\sqrt y}}-bx = \pm\color{blue}{\frac{x\sqrt{y}}{y}}-bx$$

Your answer is correct apart from the inclusion of $-bx$ in the numerator and that you didn't include the $\pm$ sign when taking the square root of both sides. As another point, you can also rationalize your answer to remove the $\sqrt y$ from the denominator, but it's not necessary.