What is the equation in standard form of the parabola with a focus at (11,-5) and a directrix of y= -19?

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What is the equation in standard form of the parabola with a focus at (11,-5) and a directrix of y= -19?

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Answer 1 · 2017-12-03T14:22:09

$y = \frac{1}{28} x^{2} - \frac{11}{14} x - \frac{215}{28}$ $y=1/28x^2-11/14x-215/28$

Explanation:

$for any point (x, y) on the parabola$ $"for any point "(x,y)" on the parabola"$

$the focus and directrix are equidistant$ $"the focus and directrix are equidistant "$

$using the distance formula$ $color(blue)"using the distance formula"$

$\sqrt{{(x - 11)}^{2} + {(y + 5)}^{2}} = | y + 19 |$ $sqrt((x-11)^2+(y+5)^2)=|y+19|$

$squaring both sides$ $color(blue)"squaring both sides"$

${(x - 11)}^{2} + {(y + 5)}^{2} = {(y + 19)}^{2}$ $(x-11)^2+(y+5)^2=(y+19)^2$

$rArrx^2-22x+121cancel(+y^2)+10y+25=cancel(y^2)+38y+361$

$rArr-28y=-x^2+22x+215$

$rArry=1/28x^2-11/14x-215/28$

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What is the equation in standard form of the parabola with a focus at (11,-5) and a directrix of y= -19?

1 Answer

Explanation:

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