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Previous Year Question (PYQs)



If any tangent to the ellipse $\frac{X^2}{a^2} + \frac{Y^2}{b^2} = 1$ intercepts equal length $l$ on both axes, then $l =$





Solution

Tangent intercept form: x/A + y/B = 1 Equal intercepts → A = B = l Condition for tangent to ellipse: 1 = a²/A² + b²/B² = a²/l² + b²/l² ⇒ l² = a² + b² ⇒ l = √(a² + b²)


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