If s = $\sqrt{(\frac{a^2}{x^2} - \frac{b^2}{y^2})}$what does y equal?

Analyze the question: We need to make y the subject of s = √(a²/x² − b²/y²).

Step 1: Square both sides

s² = a²/x² − b²/y²

Step 2: Isolate the y term

b²/y² = a²/x² − s²

Step 3: Combine the right side into one fraction

b²/y² = (a² − s²x²)/x²

Step 4: Invert both sides and solve for y²

y²/b² = x²/(a² − s²x²)

y² = b²x²/(a² − s²x²)

Step 5: Take the square root

y = √[ b²x² / (a² − s²x²) ]

Compare with the options:

• A, B, C and D do not match. They are missing the b²x² numerator and the a² − s²x² denominator.
• E: √[(b²x²)/(a² − s²x²)] matches our result exactly.

Tip: In "change of subject" questions, follow this order:

1. Remove the square root by squaring.
2. Collect the term containing the required variable on one side.
3. Combine fractions with a common denominator.
4. Invert and take the root last.

Always check that your final expression has the same structure as the options. Here the b²x² on top and the a² − s²x² below are the giveaway.