Derive the equation of the parabola with a focus at (−5, −5) and a directrix of y = 7. f(x) = −one twenty-fourth (x − 1)2 − 5 f(x) = one twenty-fourth (x − 1)2 − 5 f(x) = −one twenty-fourth (x + 5)2 + 1 f(x) = one twenty-fourth (x + 5)2 + 1

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Derive the equation of the parabola with a focus at (−5, −5) and a directrix of y = 7. f(x) = −one twenty-fourth (x − 1)2 − 5 f(x) = one twenty-fourth (x − 1)2 − 5 f(x) = −one twenty-fourth (x + 5)2 + 1 f(x) = one twenty-fourth (x + 5)2 + 1

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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if you take any point (x,y) on the curve the distance between the focus and that point = the perpendicular distance between the point and the directrix (definition of a parabola) first distance = sqrt[ (y - (-5))^2 + (x - (-5))^2] = sqrt [ (x +5)^2 + (y + 5)^2] and second distance is y - 7
so we have sqrt [ (x +5)^2 + (y + 5)^2] = (y - 7 square both sides (x +5)^2 + (y + 5)^2 = (y - 7)^2 simplify this and you'll get the required equation

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