Write a polar equation of a conic with the focus at the origin and the given data. hyperbola, eccentricity 3.5, directrix y =2
Answer:
r = 14/(2 + 7(sinθ))
Step-by-step explanation:
We are given;
Eccentricity;e = 3.5
Directrix; y = 2
This means that d = 2
We are told that the focus is at the origin, so since the directrix is at y = 2,then the part of the hyperbola that is closest to this focus will open downwards and the equation is given by;
r = ed/(1 + e•sinθ)
Plugging in the relevant values, we have;
r = (3.5 × 2)/(1 + 3.5(sinθ))
r = 7/(1 + 3.5(sinθ))
To make every figure a whole number, let's multiply numerator and denominator by 2 to give;
