Question:
The square of the slope of a common tangent to the circle \(4x^2 + 4y^2 = 25\) and ellipse \(4x^2 + 9y^2 = 36\) is
The square of the slope of a common tangent to the circle \(4x^2 + 4y^2 = 25\) and ellipse \(4x^2 + 9y^2 = 36\) is
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Use condition of common tangents: \(r^2 = \dfrac{a^2 m^2 + b^2}{m^2 + 1}\) to find \(m^2\).
Updated On: Jun 4, 2025
- \(1\)
- \(\dfrac{9}{11}\)
- \(\dfrac{2}{3}\)
- \(2\)
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The Correct Option is B
Solution and Explanation
Use combined condition for common tangents to circle and ellipse: equate expressions with slope \(m\), then simplify to get \(m^2\)
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