Question

The foci of the ellipse \[ 9x^2+25y^2=225 \] are

• A. \((\pm 4,0)\)
• B. \(\left(\pm \frac{4}{5},0\right)\)
• C. \(\left(\pm \frac{12}{5},0\right)\)
• D. \(\left(\pm \frac{2}{5},0\right)\)

Hint:

For the ellipse \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, \] the foci are obtained using \[ c^2=a^2-b^2. \] If the larger denominator is under \(x^2\), then the foci are \((\pm c,0)\).

Answer 1

The Correct Option is A

Step 1: Write in standard form.
\(9x^2+25y^2=225 \Rightarrow \dfrac{x^2}{25}+\dfrac{y^2}{9}=1\). So \(a^2=25,\; b^2=9\).

Step 2: Find c and the foci.
\(c^2 = a^2-b^2 = 25-9 = 16 \Rightarrow c=4\). Foci at \((\pm 4,\; 0)\).
\[ \boxed{(\pm 4,\; 0)} \]