The equation of the chord, of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$, whose mid-point is $(3,1)$ is :
JEE · Math · previous-year question
- A.$5 x+16 y=31$
- B.$48 x+25 y=169$correct
- C.$4 x+122 y=134$
- D.$25 x+101 y=176$
Answer
B. $48 x+25 y=169$
Explanation
$$\begin{aligned} &\text { Equation of chord with given middle point }\\ &\begin{aligned} & \mathrm{T}=\mathrm{S}_1 \\ & \Rightarrow \frac{3 \mathrm{x}}{25}+\frac{\mathrm{y}}{16}-1=\frac{9}{25}+\frac{1}{16}-1 \\ & 48 \mathrm{x}+25 \mathrm{y}=144+25 \\ & 48 \mathrm{x}+25 \mathrm{y}=169 \text { Ans. } \end{aligned} \end{aligned}$$
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