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  • The equation of the director circle of the parabola <img alt="\mathrm{y^2+4 y+4 x+2=0 }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7By%5E2&plus;4%20y&plus;4%20x&plu

The equation of the director circle of the parabola \mathrm{y^2+4 y+4 x+2=0 } is

 

Option: 1

\mathrm{x=-1}


Option: 2

\mathrm{x=1}


Option: 3

\mathrm{x=\frac{-3}{2}}


Option: 4

\mathrm{x=\frac{3}{2}}


Answers (1)

best_answer

We can write the equation of the given parabola as
\mathrm{ (y+2)^2=-4\left(x-\frac{1}{2}\right) }shifting the origin \mathrm{ \left(\frac{1}{2},-2\right) }, the equation of parabola becomes \mathrm{ Y^2=-4 X, } where \mathrm{X=x-1 / 2, Y=y+2}

Equation of director circle of parabola is same as directrix of parabola.

An equation of its directrix is \mathrm{X=1}.

Hence required directrix is \mathrm{x=3 / 2}.

Hence option 4 is correct.

Posted by

rishi.raj

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