Verified Solution • 2025–26 Session moderate

QJEEM25Maec73: JEE Main 2025 Mathematics - Class 11 JEEM25Maec73 Solution: The equation of the chord, of the ellipse , whose mid-point is…

The equation of the chord, of the ellipse x225+y216=1\frac{x^2}{25}+\frac{y^2}{16}=1 , whose mid-point is (3,1)(3,1) is :

Multiple Choice Options

  • A 5x+16y=315 x+16 y=31
  • B 48x+25y=16948 x+25 y=169
  • C 4x+122y=1344 x+122 y=134
  • D 25x+101y=17625 x+101 y=176

Step-by-Step Verified Solution

amp; Equation of chord with given middle point amp;amp;T=S1amp;⇒3x25+y16−1=925+116−1amp;48x+25y=144+25amp;48x+25y=169 Ans. \begin{aligned}&\text { Equation of chord with given middle point }\\&\begin{aligned}& \mathrm{T}=\mathrm{S}_1 \\& \Rightarrow \frac{3 \mathrm{x}}{25}+\frac{\mathrm{y}}{16}-1=\frac{9}{25}+\frac{1}{16}-1 \\& 48 \mathrm{x}+25 \mathrm{y}=144+25 \\& 48 \mathrm{x}+25 \mathrm{y}=169 \text { Ans. }\end{aligned}\end{aligned}

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