Solve (x a)^2 (y b)^2=r^2

Evaluate

(x a)^{2} (y b)^{2} = r^{2}

Multiply the terms

x^{2} a^{2} y^{2} b^{2} = r^{2}

Rewrite the expression

a^{2} y^{2} b^{2} x^{2} = r^{2}

Divide both sides

\frac{a ^{2} y ^{2} b ^{2} x ^{2}}{a ^{2} y ^{2} b ^{2}} = \frac{r ^{2}}{a ^{2} y ^{2} b ^{2}}

Divide the numbers

x^{2} = \frac{r ^{2}}{a ^{2} y ^{2} b ^{2}}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{r ^{2}}{a ^{2} y ^{2} b ^{2}}

Simplify the expression

More Steps

x = \pm \frac{∣ r ∣}{∣ a y b ∣}

Remove the absolute value bars

x = \pm \frac{r}{∣ a y b ∣}

Solution

x = \frac{r}{∣ a y b ∣} x = - \frac{r}{∣ a y b ∣}

Solve the equation