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

Question

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

(1) \(48 x+25 y-169=0\)

(2) \(25 x+5 y-125=0\)

(3) \(65 x+2 y-12=0\)

(4) \(45 x+4 y-135=0\)

Answer 1

Correct option is (1) \(48 x+25 y-169=0\)  

Chord with given mid-point 

\(\Rightarrow T=S_1 \)  

\(\Rightarrow\left(\frac{x x_1}{25}+\frac{yy_1}{16}-1\right)=\frac{x_1^2}{25}+\frac{y_1^2}{16}-1 \)   

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

\(\Rightarrow 48 x+25 y-400=144+25-400 \)  

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