The equation of the chord, of the ellipse x^2/25+y^2/16=1, whose mid-point is (3, 1) is :

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 :

(1) \(48 x+25 y=169\)

(2) \(4 x+122 y=134\)

(3) \(25 x+101 y=176\)

(4) \(5 x+16 y=31\)
 

Answer 1

Correct option is (1) \(48 x+25 y=169\)  

Equation of chord with given middle point

\(\mathrm{T}=\mathrm{S_1}\)

\(\Rightarrow \frac{3 \mathrm{x}}{25}+\frac{\mathrm{y}}{16}-1=\frac{9}{25}+\frac{1}{16}-1\)

\(48 \mathrm{x}+25 \mathrm{y}=144+25\)

\(48 \mathrm{x}+25 \mathrm{y}=169\)