Find the polar equation of the conic with the focus at the pole, directrix y = -6, and eccentricity 4 (picture provided)
1 answer:
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;
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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Answer:
Step-by-step explanation:
The square is in the circle, so the diameter is the diagonal line of the square. This divides the square into two right triangles.
Two sides of the right triangle equal 8. This qualifies it as a special right triangle. This triangle has two sides that = x (in this case 8) and the hypotenuse is .
Substitute 8 in for x.
is the diameter, so we divide in half to get the radius =