InterviewSolution
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InterviewSolution
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If the circle `x^2+y^2=a^2` intersects the hyperbola `xy=c^2` in four points `P(x_1,y_1)`,`Q(x_2,y_2)`,`R(x_3,y_3)`,`S(x_4,y_4)`, then which of the following need not hold.(a) `x_1+x_2+x_3+x_4=0`(b) `x_1 x_2 x_3 x_4=y_1 y_2 y_3 y_4=c^4`(c) `y_1+y_2+y_3+y_4=0`(d) `x_1+y_2+x_3+y_4=0`A. `x_(1)+x_(2)+x_(3)+x_(4)=01`B. `y_(1)+y_(2)+y_(3)+y_(4)=0`C. `x_(1)x_(2)+x_(3)x_(4)=c^(4), y_(1)y_(2)y_(3)y_(4)=c^(4)`D. all of these |
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Answer» Correct Answer - D The x-coordinates of P, Q, R and S are the roots of the equation `x^(2)+((c^(2))/(x))^(2)=a^(2)rArr x^(4)+0x^(3)-a^(2)x^(2)+0x+c^(4)=0` `:. x_(1)+x_(2)+x_(3)+x_(4)=0 and x_(1)x_(2)x_(3)x_(4)=c^(4)` Similarly , y-coordinates are the roots of the equation `y^(2)+((c^(2))/(y))^(2)=a^(2) rArr y^(4) + 0y^(3)-a^(2)y^(2)+0y+c^(4)=0` This give that `y_(1)+y_(2)+y_(3)+y_(4)=0 and y_(1)y_(2)y_(3)y_(4)=c^(4)` Hence, all the options are correct. |
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