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daser333 [38]
2 years ago
14

27. Find a polar equation of the conic with focus at the pole that has the given eccentricity and equation of directrix.

Mathematics
1 answer:
ololo11 [35]2 years ago
4 0

The polar equation will be  r=\dfrac{4}{1+cos\theta}

<h3> What is the polar equation?</h3>

A polar equation is any equation that expresses the relationship between r and theta, where r is the distance between the pole (origin) and a point on a curve, and theta is the counterclockwise angle formed by a point on a curve, the pole, and the positive x-axis.

From the equation, we are told that

The  Eccentricity: e = 1

The  Directrix is   y = 4

Generally, the polar equation for e =  1  and y  =  + c is mathematically represented as

r =\dfrac{e\times c}{1+ecos\theta}

r =\dfrac{1\times 4}{1+1\times cos\theta}  

 r=\dfrac{4}{1+cos\theta}

 

Therefore the polar equation will be  r=\dfrac{4}{1+cos\theta}

To know more about the polar equation follow

brainly.com/question/9363127

#SPJ1

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The diagram is below

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Let's find the distance from A to B using the distance formula.

d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-2)^2 + (-1-1)^2}\\\\d = \sqrt{(-2)^2 + (-2)^2}\\\\d = \sqrt{4 + 4}\\\\d = \sqrt{8}\\\\d \approx 2.828\\\\

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Through very similar steps, you should find that the other side lengths of BC, CD and AD are all the same.

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-----------------------------

Let's find the slope of line AB

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - (-1)}{2 - 0}\\\\m = \frac{1 + 1}{2 - 0}\\\\m = \frac{2}{2}\\\\m = 1\\\\

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Therefore, this figure is a rectangle. Any rectangle has all four angles of 90 degrees.

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The first section showed that we have a rhombus. The second section afterward showed that we also have a rectangle. The combination of a rhombus and a rectangle at the same time leads to a square.

Therefore, quadrilateral ABCD is a square.

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Answer:

B. X4+ 4x2 +8x is the answer

Step-by-step explanation:

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