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The following equation is a conic section written in polar coordinates.=51 + 5sin(0)Step 2 of 2: Find the equation for the directrix of the conic section.

The Following Equation Is A Conic Section Written In Polar Coordinates51 5sin0Step 2 Of 2 Find The Equation For The Directrix Of The Conic Section class=

Sagot :

For a conic with a focus at the origin, if the directrix is

[tex]y=\pm p[/tex]

where p is a positive real number, and the eccentricity is a positive real number e, the conic has a polar equation

[tex]r=\frac{ep}{1\pm e\sin\theta}[/tex]

if 0 ≤ e < 1 , the conic is an ellipse.

if e = 1 , the conic is a parabola.

if e > 1 , the conic is an hyperbola.

In our problem, our equation is

[tex]r=\frac{5}{1+5\sin\theta}[/tex]

If we compare our equation with the form presented, we have

[tex]\begin{cases}e={5} \\ p={1}\end{cases}[/tex]

Therefore, the directrix is

[tex]y=1[/tex]

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