New Notes Blog: `x^2=-36y` Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola.

Saturday, 10 May 2014

$\displaystyle{{x}}^{{2}}=-{36}{y}$ Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola.

Let $\displaystyle{{x}}^{{2}}={4}{p}{y}$ be equation of parabola. Then equation of directrix is $\displaystyle{y}=-{p}$ coordinates of focus are $\displaystyle{\left({0},{p}\right)}$ and axis of symmetry is $\displaystyle{y}$ -axis.

In this case the equation of parabola is

$\displaystyle{{x}}^{{2}}=-{36}{y}$

Therefore,

$\displaystyle{4}{p}=-{36}$

$\displaystyle{p}=-{9}$

Using the facts stated above we can write equation of directrix and coordinates of focus.

Directrix is line with equation $\displaystyle{y}={9},$ focus is the point with coordinates $\displaystyle{\left({0},-{9}\right)}$ and axis of symmetry is $\displaystyle{y}$ -axis.

In this case the equation of parabola is

$\displaystyle{{x}}^{{2}}=-{36}{y}$

Therefore,

$\displaystyle{4}{p}=-{36}$

$\displaystyle{p}=-{9}$

Using the facts stated above we can write equation of directrix and coordinates of focus.

Directrix is line with equation $\displaystyle{y}={9},$ focus is the point with coordinates $\displaystyle{\left({0},-{9}\right)}$ and axis of symmetry is $\displaystyle{y}$ -axis.

New Notes Blog

Saturday, 10 May 2014

$\displaystyle{{x}}^{{2}}=-{36}{y}$ Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola.

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In "By the Waters of Babylon," under the leadership of John, what do you think the Hill People will do with their society?

Saturday, 10 May 2014

Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola.

No comments:

Post a Comment

In &quot;By the Waters of Babylon,&quot; under the leadership of John, what do you think the Hill People will do with their society?

$\displaystyle{{x}}^{{2}}=-{36}{y}$ Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola.

In "By the Waters of Babylon," under the leadership of John, what do you think the Hill People will do with their society?