Question:medium
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 25, 2026
- \( 4x + 122y = 134 \)
- \( 25x + 101y = 176 \)
- \( 5x + 16y = 31 \)
- \( 48x + 25y = 169 \)
Show Solution
The Correct Option is C
Solution and Explanation
The chord of an ellipse can be determined using its midpoint and the ellipse's equation. Substituting these into the midpoint formula allows us to derive the equation of the chord.
Final Answer: \( 5x + 16y = 31 \).
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