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Question:
If the lines joining the focii of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) where a>b and an extremity of its minor axis is inclined at an angle 60°, then the eccentricity of the ellipse is
If the lines joining the focii of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) where a>b and an extremity of its minor axis is inclined at an angle 60°, then the eccentricity of the ellipse is
Updated On: Apr 27, 2024
- \(\frac{\sqrt3}{2}\)
- \(\frac{1}{2}\)
- \(\frac{\sqrt7}{3}\)
- \(\frac{1}{\sqrt3}\)
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The Correct Option is B
Solution and Explanation
The correct answer is option (B): \(\frac{1}{2}\)
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Concepts Used:
Conic Sections
When a plane intersects a cone in multiple sections, several types of curves are obtained. These curves can be a circle, an ellipse, a parabola, and a hyperbola. When a plane cuts the cone other than the vertex then the following situations may occur:
Let ‘β’ is the angle made by the plane with the vertical axis of the cone
- When β = 90°, we say the section is a circle
- When α < β < 90°, then the section is an ellipse
- When α = β; then the section is said to as a parabola
- When 0 ≤ β < α; then the section is said to as a hyperbola
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