Find the standard form of the equation of the parabola

Ответ:

Jorjalilli1318

15.01.2022

The standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2 is $y=\frac{1}{8}x^2$ .

Step-by-step explanation:

The standard form of the parabola is

y=ax^2+bx+c

The general form of the parabola is

(x-h)^2=4p(y-k) ..... (1)

Where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.

It is given that the parabola with a focus at (0, 2) and a directrix at y = -2. It means

(h,k+p)=(0,2)

h=0

k+p=2 .... (2)

$y=k-p\Rightarrow k-p=-2$ .... (3)

On solving (2) and (3), we get

k=0

p=2

Substitute h=0, k=0 and p=2 in equation (1).

(x-0)^2=4(2)(y-0)

x^2=8y

Divide both sides by 8.

$\frac{1}{8}x^2=y$

Therefore the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2 is $y=\frac{1}{8}x^2$ .

0,0(0 оценок)