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4 years ago

How would you write y - 3 = 1/2 (x + 4) in standard form?

Mathematics

1 answer:

Vesnalui [34]4 years ago

5 0

Y - 3 = 1/2 (x + 4)
y - 3 = 1/2 x + 2
1/2x + 2 = y - 3
1/2x - y = -3 - 2
1/2x - y = -5 answer

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A parabola can be represented by the equation x2 = -20y.

aliya0001 [1]

Answer:

$\mathrm{Parabola\:focus\:given}\:x^2=-20y:\quad \left(0,\:-5\right)$

Step-by-step explanation:

Given the equation

$x2 = -20y$

A parabola is the locus of points such that the distance to a point the focus equals the distance to a line the directrix.

$4p\left(y-k\right)=\left(x-h\right)^2$ is the standard equation for an up-down facing parabola with vertex at (h, k), and a focal length |p|.

$x^2=-20y$

$\mathrm{Switch\:sides}$

$-20y=x^2$

$\mathrm{Factor\:}4$

$4\cdot \frac{-20}{4}y=x^2$

$4\left(-5\right)y=x^2$

$\mathrm{Rewrite\:as}$

$4\left(-5\right)\left(y-0\right)=\left(x-0\right)^2$

$\left(h,\:k\right)=\left(0,\:0\right),\:p=-5$

Parabola is symmetric around the y-axis and so the focus lies a distance\ p from the center (0, 0) along the y-axis.

$\left(0,\:0+p\right)$

$=\left(0,\:0+\left(-5\right)\right)$

$\mathrm{Refine}$

$\left(0,\:-5\right)$

Therefore,

$\mathrm{Parabola\:focus\:given}\:x^2=-20y:\quad \left(0,\:-5\right)$

Please check the attached figure too.

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