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Consider the family of conic curves $x^{2} \cos θ + y^{2} \sin θ = 1$ , where $θ = \frac{(k - 1) π}{12}$ and $k$ is determined by summing the output of two fair dice rolled simultaneously. What is the probability that the curve is an ellipse or a Hyperbola,

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$\frac{1}{3}$

$\frac{4}{9}$

$\frac{5}{6}$

$\frac{3}{4}$

answer is D.

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Detailed Solution

Value of $k$	No. of outcomes	Type of conic
2	1	Ellipse
3	2	Ellipse
4	3	circles
5	4	Ellipse
6	5	Ellipse
7	6	Pair of lines
8	5	Hyperbola
9	4	Hyperbola
10	3	Hyperbola
11	2	Hyperbola
12	1	Hyperbola

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