InterviewSolution
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InterviewSolution
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The straight line`x/a+y/b=1`cuts the coordinate axes at `A`and `B`. Find the equation of the circle passing through `O(0,0),Aa n dBdot`A. `x^(2)+y^(2)-ax-by=0`B. `x^(2)+y^(2)-2ax-2by=0`C. `x^(2)+y^(2)+ax+by=0`D. `x^(2)+y^(2)=a^(2)+b^(2)` |
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Answer» Correct Answer - A The straight line `(x)/(a)+(y)/(b)=1` cuts the coordinate axes at A(a, 0) and B(0, b). Let `x^(2)+y^(2)+2gx+2fy+c=0 " " ...(i)` be the circle passing through O, A and B. Then, `0+c=0 " " (ii)` `a^(2)+2ga+c=0 " " ...(iii)` `b^(2)+2fb+c=0 " " (iv)` Solving (ii), (iii) and (iv), we obtain `g=-(a)/(2), f=-(b)/(2)` and `c=0` Substituting these values in (i), we obtain the equation of the required circle as `x^(2)+y^(2)-ax-by=0` |
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