# How do you write the standard equation for a parabola with the given vertex (3,3) and focus: (-2,3)?

Mar 31, 2017

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Mar 31, 2017

$x = - {y}^{2} / 20 + \frac{3 y}{10} + \frac{51}{20}$

#### Explanation:

Here as the ordinate of vertex and focus is same , axis of symmetry is $y = 3$ and equation of parabola is of the form

$4 p \left(x - 3\right) = {\left(y - 3\right)}^{2}$

As such its focus is $\left(3 + p , 3\right)$ and as focus is $\left(- 2 , 3\right)$

we have $p = - 5$ and equation of parabola is

$- 20 \left(x - 3\right) = {\left(y - 3\right)}^{2}$

or $x = - \frac{1}{20} \left({y}^{2} - 6 y + 9\right) + 3$

or $x = - {y}^{2} / 20 + \frac{3 y}{10} + \frac{51}{20}$

graph{x=-y^2/20+(3y)/10+51/20 [-52.5, 27.5, -16.64, 23.36]}