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(i) If a, b, c, are in A.P. then show that ax….+….by +c=0 passes through a fixed point. Find then fixed point. (ii)If 9a^(2)+16b^(2)-24ab-25c^(2)=0, then the family of straight lines ax+by+0 is concurrent at the point whose co-ordinates are given by "________" (iii) If 3a+4b-5c=0, then the family of straight lines ax+by+c=0 passes through a fixed point. Find the coordinates of the point. |
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Answer» Solution :(i) a,b,c are in A.P. `impliesa-2b+c=0` Comparing the given equation `ax+by+c=0` with `a-2b+c=0` we find that the straight line `ax+by6+c=0` passes through the fixed point `(1,-2).` (ii) We have, `9a^(2)+16b^(2)-24ab-25c^(2)=0` `implies(3a-4b)^(2)-(5c)^(2)=0` `implies(3a-4b+5c)(3a-4b-5c)=0` `implies((3)/(5)a-(4)/(5)b+c)((-3)/(5)a+(4)/(5)b+c)=0` `implies` The FAMILY of lines `ax+by+c=0` is either concurrent at `((3)/(5),(-4)/(5))or (-(3)/(5),(4)/(5))` (III) We have, `3a+4b-5c=0` `implies-(3)/(5)a-(4)/(5)b+c=0` `implies` The given family of lines `ax+by+x=0` passes through the fixed point `((-3)/(5),(-4)/(5)).` |
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