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write the equations of these parabolas in vertex form: • focus at (-5,-3), and directrix y = -6 • focus at (10,-4), and directrix y = 6​

Sagot :

Answer:

y=0.12/1(x-5)^2 -3

y=1/10(x-10)^2 -4

Step-by-step explanation:

Given the directrix and focus of the parabolas, the equation of the parabolas are [tex]y=\frac{1}{6}(x^{2} +10x - 2)[/tex] and [tex]y=\frac{1}{20}(-x^{2} +20x - 80)[/tex].

What is equation of a parabola?

Equation of a parabola is given by-

Distance of a point (x, y) on parabola from directrix =  Distance of a point (x, y) on parabola from focus

focus = (-5, -3)

directrix = y = -6

[tex]\sqrt{(x+5)^{2}+(y+3)^{2} } = (y+6)\\\\ (x+5)^{2}+(y+3)^{2} = (y+6)^{2}\\\\x^{2} +25+5x = 6y+27\\\\y=\frac{1}{6}(x^{2} +10x - 2)[/tex]

focus = (10,-4)

directrix = y = 6

[tex]\sqrt{(x-10)^{2}+(y+4)^{2} } = (y-6)\\\\ (x-10)^{2}+(y+4)^{2} = (y-6)^{2}\\\\x^{2} +100-20x = -20y+20\\\\y=\frac{1}{20}(-x^{2} +20x - 80)[/tex]

Learn more about equation of parabola here

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