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tia_tia [17]
2 years ago
14

Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1

Mathematics
1 answer:
geniusboy [140]2 years ago
5 0

Answer:

Step-by-step explanation:

eq. of directrix is y-1=0

let (x,y) be any point the parabola.

then\sqrt{ (x-6)^2+(y-2)^2}=\frac{y-1}{(-1)*2}

squaring

x²-12x+36+y²-4y+4=y²-2y+1

x²-12 x+40-1=4y-2y

2y=x²-12x+39=x²-12x+36+3

(x-6)²=2y-3

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Is y= 1/2x - 4 equal to 3x - 6y = 24
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Answer:

\fbox{\begin{minipage}{4em}Yes, it is\end{minipage}}

Step-by-step explanation:

3x - 6y = 24

Divide both sides by 6:

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Simplify:

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Move y to the right side, 4 to the left side, and change sign of y and 4:

(1/2)x - 4 = y

Rearrange both sides:

y= (1/2)x - 4

Hope this helps!

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