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A focus of an ellipse is at the origi...

A focus of an ellipse is at the origin. The directrix is the line `x""=""4` and the eccentricity is 1/2. Then the length of the semimajor axis is (1) `8/3` (2) `2/3` (3) `4/3` (4) `5/3`

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To solve the problem step by step, we will use the properties of an ellipse, focusing on the relationship between the focus, directrix, eccentricity, and the semi-major axis. ### Step 1: Understand the given information - Focus (F) of the ellipse is at the origin (0, 0). - Directrix (D) is the line \( x = 4 \). - Eccentricity (e) is given as \( \frac{1}{2} \). ### Step 2: Use the relationship between the semi-major axis (A), eccentricity (e), and directrix ...
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Knowledge Check

  • A focus of an ellipse is at the origin. The directrix is the line x=4 and the eccentricity is 1/2: Then the length of the semi-major axis is :

    A
    `8/3`
    B
    `2/3`
    C
    `4/3`
    D
    `5/3`

  • The focus of an ellipse is at the origin. If the directrix is the line x=5 and the eccentricity is 1/3 , then find the length of major axis.

    A
    `(15)/4`
    B
    `(15)/2`
    C
    `(15)/8`
    D
    None of these

  • If question of the ellipse whose focus is (1,-1), then directrix the line x-y-3=0 and eccentricity 1/2 is

    A
    `7x^(2)+2xy+7y^(2)-10x+10y+7=0`
    B
    `7x^(2)+2xy+7y^(2)+7=0`
    C
    `7x^(2)+2xy+7y^(2)+10x-10y-7=0`
    D
    `"none of these"`

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