Solve ay^2-4=y^2+1

$$a y ^ { 2 } - 4 = y ^ { 2 } + 1$$

Solve for a

$$a=1+\frac{5}{y^{2}}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Add 4 to both sides.

$$ay^{2}=y^{2}+1+4$$

Add 1 and 4 to get 5.

$$ay^{2}=y^{2}+5$$

The equation is in standard form.

$$y^{2}a=y^{2}+5$$

Divide both sides by y^{2}.

$$\frac{y^{2}a}{y^{2}}=\frac{y^{2}+5}{y^{2}}$$

Dividing by y^{2} undoes the multiplication by y^{2}.

$$a=\frac{y^{2}+5}{y^{2}}$$

Divide y^{2}+5 by y^{2}.

$$a=1+\frac{5}{y^{2}}$$

Solve for y

$$y=\sqrt{\frac{5}{a-1}}$$

$$y=-\sqrt{\frac{5}{a-1}}\text{, }a>1$$