If the eccentricity of the hyperbola (x^2)/(1+sin⁡θ^2)-(y^2)/(cos^2⁡θ)=1 is 2/(√3), then the sum of all the possible values of θ is (where, θ∈0,π)

Question

MARKS Content Team · Accepted Answer

Correct answer: (D) π. e^2=1+(cos^2⁡θ1+sin⁡θ^2=43⇒cos^2⁡θ1+sin⁡θ^2=13⇒cos⁡θ1+sin⁡θ^2=13⇒sin⁡π2-θ1+cos⁡π2-θ^2=13⇒tan^2⁡π)/4-(θ)/2=1/3 (π)/4-(θ)/2=(-π)/6,(π)/6⇒(θ)/2=(π)/4-(π)/6,(π)/4+(π)/6 θ=(π)/2±(π)/3=(π)/6,(5π)/6 Hence, the required sum =π

If the eccentricity of the hyperbola $\frac{x^{2}}{{(1 + \sin θ)}^{2}} - \frac{y^{2}}{\cos^{2} θ} = 1$ is $\frac{2}{\sqrt{3}},$ then the sum of all the possible values of $θ$ is (where, $θ \in (0, π)$ )

Solution

More Hyperbola Questions

If the eccentricity of the hyperbola x21+sin⁡θ2-y2cos2⁡θ=1 is 23, then the sum of all the possible values of θ is (where, θ∈0,π)

Solution

More Hyperbola Questions

If the eccentricity of the hyperbola $\frac{x^{2}}{{(1 + \sin θ)}^{2}} - \frac{y^{2}}{\cos^{2} θ} = 1$ is $\frac{2}{\sqrt{3}},$ then the sum of all the possible values of $θ$ is (where, $θ \in (0, π)$ )