A parabola can be drawn given a focus of (8,7) and a directrix of x = −2. What can be said about the parabola?

Mathematics

1 answer:

krek1111 [17]2 years ago

5 0

Answer:

See below

Step-by-step explanation:

Given that the directrix is vertical, the parabola has to be horizontal because its axis is perpendicular to the directrix.

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One day, a person went to a horse racing area. Instead of counting the number of humans an horses, he conuted 74 heads and 196 l

BigorU [14]

X = the number of humans and y = the number of horses.

x+y=74
2x+4y=196

Because the number of humans and horses together is 74, and the total number of legs (2 per every human, x, and 4 per every horse, y) is 196. Then, just use elimination to solve.

$-2(x+y=74)\\2x+4y=196\\\\-2x-2y=-148\\2x+4y=196\\\\2y=48\\y=24$

So, now that you have y, you can plug it into the first equation to find x:

$x+y=74\\x+24=74\\x=50$

So, x = 50 and y = 24, so there are 50 humans and 24 horses.
The correct answer is B.

4 0

3 years ago

Which equation represents the equation of the parabola with focus (-3 3) and directrix y=7?

Artemon [7]

Answer:

The equation $y=\frac{-x^2-6x+31}{8}$ represents the equation of the parabola with focus (-3, 3) and directrix y = 7.

Step-by-step explanation:

To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).

Using the distance formula $d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$ , we find that the distance between (x, y) is

$\sqrt{(x+3)^2+(y-3)^2}$

and the distance between (x, y) and the directrix y = 7 is

$\sqrt{(y-7)^2}$ .

On the parabola, these distances are equal so, we solve for y:

$\sqrt{(x+3)^2+(y-3)^2}=\sqrt{(y-7)^2}\\\\\left(\sqrt{\left(x+3\right)^2+\left(y-3\right)^2}\right)^2=\left(\sqrt{\left(y-7\right)^2}\right)^2\\\\x^2+6x+y^2+18-6y=\left(y-7\right)^2\\\\x^2+6x+y^2+18-6y=y^2-14y+49\\\\y=\frac{-x^2-6x+31}{8}$