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krok68 [10]
2 years ago
11

Find the polar equation of the conic with the focus at the pole, directrix y = -6, and eccentricity 4 (picture provided)

Mathematics
1 answer:
Keith_Richards [23]2 years ago
5 0

Answer:

Choice B is correct

Step-by-step explanation:

The eccentricity of the conic section is given as 4 and thus the conic section is a hyperbola. Hyperbolas are the only conic sections with an eccentricity greater than 1.

Next, the directrix of this hyperbola is located at y = -6 implying that the hyperbola will be opening upwards. Consequently, the polar equation of this hyperbola will be of the form;

r=\frac{k}{1-4sin(theta)}

The value of k in the numerator is the product of eccentricity and the absolute value of the directrix;

k= 4*6 = 24

The polar equation is thus given by alternative B

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Hi there!  

»»————- ★ ————-««

I believe your answer is:  

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»»————- ★ ————-««  

Here’s why:  

  • We can use inverse operations to solve for 'm'.

⸻⸻⸻⸻

\boxed{\text{Solving for 'm':}}\\\\5m+1\leq4\\--------\\\rightarrow 5m + 1 - 1 \leq 4 - 1\\\\\rightarrow 5m\leq3\\\\\rightarrow \frac{5m\leq3}{5}\\\\\rightarrow \boxed{m\leq\frac{3}{5}}

⸻⸻⸻⸻

Any number that is less than or equal to the value of three-fifths would work.

The option that is less than or equal to (3/5) is option A.

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»»————- ★ ————-««  

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