Solve (x h)^2 (y k)^2=r^2

Evaluate

(x h)^{2} (y k)^{2} = r^{2}

Multiply the terms

x^{2} h^{2} y^{2} k^{2} = r^{2}

Rewrite the expression

h^{2} y^{2} k^{2} x^{2} = r^{2}

Divide both sides

\frac{h ^{2} y ^{2} k ^{2} x ^{2}}{h ^{2} y ^{2} k ^{2}} = \frac{r ^{2}}{h ^{2} y ^{2} k ^{2}}

Divide the numbers

x^{2} = \frac{r ^{2}}{h ^{2} y ^{2} k ^{2}}

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

x = \pm \frac{r ^{2}}{h ^{2} y ^{2} k ^{2}}

Simplify the expression

More Steps

x = \pm \frac{∣ r ∣}{∣ h y k ∣}

Remove the absolute value bars

x = \pm \frac{r}{∣ h y k ∣}

Solution

x = \frac{r}{∣ h y k ∣} x = - \frac{r}{∣ h y k ∣}

Solve the equation