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Ellipse

Director Circle

Premium Question

Grade 11

Question:

The director circle of the ellipse $\frac{x^2}{25} + \frac{y^2}{9} = 1$ is:

(1) $x^2 + y^2 = 25$

(2) $x^2 + y^2 = 9$

(3) $x^2 + y^2 = 34$

(4) $x^2 + y^2 = 16$

Step-by-Step Solution

Key Concept: The director circle of $x^2/a^2 + y^2/b^2 = 1$ is $x^2 + y^2 = a^2 + b^2 = 25 + 9 = 34$.

The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.

Correct Answer: (3)