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If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0respresent the pair of parallel straight lines , then prove that h^(2)=abandabc+2fgh-af^(2)-bg^(2)-ch^(2)=0. |
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Answer» SOLUTION :Let the given equation represent PAIR of parallel straigh lines `lx+my+n=0andlx+my+n'=0` `:. ax^(2)+2HXY+b^(2)+2gx+2fy+c` `=(lx+my+n)(lx+my+n')` `=(lx+my)^(2)+L(n+n')x+m(n+n')y+nn'=0` Thus , expression`(lx+my)^(2)` is same as `ax^(2)+by^(2)_2hxy`. Therefore , `ax^(2)+2hxy+by^(2)`must be perfect SQUARE of liner expression inx and y. So `(2h)^(2)-4ab=0` `:. h^(2)=ab` Also , `abc+2ghf-af^(2)-bg^(2)-ch^(2)=0`. |
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