Question

A parabola can be drawn given a focus of (-5, -8)(−5,−8) and a directrix of y=-4y=−4. Write the equation of the parabola in any form.

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Answer 1

`y=-(1)/(8) x^2-(5)/(4) x-(73)/(8).`

Explanation:

1) according to the definition of parabola two distance are equal, then:

2) d1=y+4 and d2=sqrt[(x+5)²+(y+8)²]; then

3) sqrt[(x+5)²+(y+8)²]=|y+4|;

(x+5)²+(y+8)²=(y+4)²; ⇔ x²+10x+73=-8y or

y=-1/8 x² -5/4 x -73/8.