Question:
The equation of the chord of the ellipse \( \frac{x^2}{25} + \frac{y^2}{16} = 1 \), whose mid-point is \( (3, 1) \) is:
The equation of the chord of the ellipse \( \frac{x^2}{25} + \frac{y^2}{16} = 1 \), whose mid-point is \( (3, 1) \) is:
Show Hint
To find the equation of a chord with a known midpoint, use the midpoint formula and substitute into the equation of the ellipse to find the required chord equation.
Updated On: Mar 20, 2025
- \( 4x + 122y = 134 \)
- \( 25x + 101y = 176 \)
- \( 5x + 16y = 31 \)
- \( 48x + 25y = 169 \)
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The Correct Option is C
Solution and Explanation
The equation of the chord of an ellipse can be found by using the midpoint formula. Given the midpoint and the equation of the ellipse, we substitute and solve for the equation of the chord.
Final Answer: \( 5x + 16y = 31 \).
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