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  • A parabola has its focus at the point (-2, 0) and its directrix is the line x = 2. Find the equation of the parabola.Option: 1 <img alt="\m

A parabola has its focus at the point (-2, 0) and its directrix is the line x = 2. Find the equation of the parabola.

Option: 1

\mathrm{y^2=-4 x+4}
 


Option: 2

\mathrm{y^2=-8 x}
 


Option: 3

\mathrm{y^2=-4 x-4}
 


Option: 4

\mathrm{y^2=8 x}


Answers (1)

best_answer

the directrix is horizontal, use the equation of a parabola that opens left or right.

\mathrm{ \left.(y-k)^2=4 p(x-h)\right)}
The vertex is \mathrm{\left(\frac{-2+2}{2}, 0\right).}

Distance from the focus to the vertex is \mathrm{\mathrm{p}-2.}

Substitute the value in the equation \mathrm{ \left.(y-k)^2=4 p(x-h)\right)}

So, \mathrm{(y-0)^2=4(-2)(x-0)}

\mathrm{ \Rightarrow y^2=-8 x }

The graph i given below -

Posted by

avinash.dongre

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