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Tangents \mathrm{PA} and \mathrm{PB} drawn to \mathrm{x^2+y^2=4} from point P which lie on the line \mathrm{x+y=9} then locus of mid point of chord \mathrm{A B}  is
 

Option: 1

\mathrm{4(x+y)=9\left(x^2+y^2\right) }
 


Option: 2

\mathrm{9\left(x^2+y^2\right)=4(x+y)}


Option: 3

\mathrm{2(x+y)=3\left(x^2+y^2\right)}


Option: 4

\mathrm{3\left(x^2+y^2\right)=2(x+y)}


Answers (1)

best_answer

Equation of chord of contact of \mathrm{P(t, 9-t)} is \mathrm{t x+y(9-t)=4}

Equation of chord whose mid point is \left(\mathrm{x}_1, \mathrm{y}_1\right) is \mathrm{xx}_1+\mathrm{yy}_1=\mathrm{x}_1^2+\mathrm{y}_1^2

\mathrm{\frac{t}{x_1}=\frac{9-t}{y_1}=\frac{4}{x_1^2+y_1^2}=\frac{t+9-t}{x_1+y_1}=\frac{9}{x_1+y_1} }

Posted by

shivangi.shekhar

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