Q

# Find the equation of the parabola that satisfies the given conditions: Vertex (0,0); focus (3,0)

9. Find the equation of the parabola that satisfies the given conditions:

Vertex (0,0); focus (3,0)

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Given,

Vertex (0,0) And  focus (3,0)

As vertex of the parabola is (0,0) and focus lies in the positive X-axis, The parabola will open towards the right, And the standard equation of such parabola is

$y^2=4ax$

Here it can be seen that $a=3$

So, the equation of a parabola is

$\Rightarrow y^2=4ax\Rightarrow y^2=4(3)x$

$\Rightarrow y^2=12x$.

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