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Find the equation of line which is normal to the parabola `x^(2)=4y` and touches the parabola `y^(2)=12x`. |
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Answer» Normal to parabola `x^(2)=4y` having slope m is `y=mx+2+(1)/(m^(2))` (1) It is tangent to `y^(2)=12x`. Now, tangent to above parabola having slope m is `y=mx+(3)/(m)` (2) Comparing (1) and (2), we get `(1)/(m^(2))+2=(3)/(m)` `rArr" "2m^(2)-3m+1=0` `rArr" "(2m-1)(m-1)=0` `rArr" "m=(1)/(2)orm=1` Therefore, equations of lines are 2y=x+12 or y=x+3. |
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