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If the lines `L_1a n dL_2`are tangents to `4x^2-4x-24 y+49=0`and are normals for `x^2+y^2=72 ,`then find the slopes of `L_1`and `L_2dot` |
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Answer» As `L_(1)andL_(2)` are normals to `x^(2)+y^(2)=72`, they must be of the form y=mx. Sloving it with parabola `4x^(2)-4x-24y+49=0`, we have `4x^(2)-4x-24mx+49=0` `or4x^(2)-4x(1+6m)+49=0` Since the lines touch the parabola, D=0 `or16(6m+1)^(2)-16xx49=0` `or6m+1pm7` `i.e.,m=1or-(4)/(3)` |
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