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  • The equation of the diameter of the parabola corresponding to the system of paril

The equation of the diameter of the parabola \mathrm{y^2=12 x} corresponding to the system of parillel chords \mathrm{4 x-y+k=0} is
 

Option: 1

\mathrm{3 y+2=0}
 


Option: 2

\mathrm{2 y-3=0}
 


Option: 3

\mathrm{3 y-2=0}
 


Option: 4

\mathrm{2 y-1=0}


Answers (1)

best_answer

The locus of the mid-points of a system of parallel chords of a conic is called as its diameter and the equation of the diameter bisecting chords of slope \mathrm{m} of the parabola

\mathrm{y^2=4 a x\: is \: given\: by\: y=\frac{2 a}{m}}
In the problem, \mathrm{y^2=4(3) x}

\mathrm{\therefore a=3} and system of parallel chords is \mathrm{4 x-y+k=0}

\mathrm{\therefore m=4}

\mathrm{\therefore } Equation of diameter is \mathrm{y=\frac{2 a}{m}=\frac{2(3)}{4}=\frac{3}{2} }

\mathrm{\Rightarrow 2 y-3=0}
 

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