alleryThe standard equation of a hyperbola with centre at the origin and foci on the $x$-axis is:
A$\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$
B$\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$
C$\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 2$
D$y^2 - x^2 = 4a^2$
Answer & Solution
Correct answer: B. $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$
A hyperbola with foci on the $x$-axis has the standard form $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ — note the **minus** between the two terms (an ellipse uses a plus).
For foci on the $y$-axis the form flips: $\dfrac{y^2}{a^2} - \dfrac{x^2}{b^2} = 1$.
Keep practising Unit 8A: Areas Between Curves
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