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What will be equation of that chord of hyperbola \mathrm{25 x^2-16 y^2=400},  whose mid point is \mathrm{(5, 3)}

Option: 1

\mathrm{115 x-117 y=17}


Option: 2

\mathrm{125 x-48 y=481}


Option: 3

\mathrm{127 x+33 y=341}


Option: 4

\mathrm{15 x+121 y=105}


Answers (1)

best_answer

According to question, \mathrm{S=25 x^2-16 y^2-400=0}
Equation of required chord is \mathrm{S_{1}=T\ \ \ ..........(i)}
\mathrm{\text { Here } S_1=25(5)^2-16(3)^2-400=625-144-400=81 \text { and } T=25 x x_1-16 y y_1-400}
\mathrm{where\ x_1=5, y_1=3} \\ \mathrm{\Rightarrow 25 x(5)-16 y(3)-400=125 x-48 y-400}
So, from \mathrm{(i)} required chord is \mathrm{125 x-48 y-400=81 \Rightarrow 125 x-48 y=481}

Posted by

shivangi.bhatnagar

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