EllipseEasy
Question
For the hyperbola 
= 1, which of the following remains constant when α varies?
= 1, which of the following remains constant when α varies?Options
A.eccentricity
B.directrix
C.abscissae of vertices
D.abscissae of foci
Solution
a2 = cos2 α and b2 = sin2 α
coordinates of focii are (± ae, 0)
∴ b2 = a2(e2 - 1) ⇒ e = sec α.
Hence abscissae of foci remain constant when α varies.
coordinates of focii are (± ae, 0)
∴ b2 = a2(e2 - 1) ⇒ e = sec α.
Hence abscissae of foci remain constant when α varies.
Create a free account to view solution
View Solution FreeMore Ellipse Questions
If P is a point on the ellipse of eccentricity e and A, A′ are the vertices and S, S′ are the focii then ...If ellipses $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ be described having the same major axis, but a variable mino...If the eccentricity of the hyperbola x2 - y2 sec2θ = 4 is √3 times the eccentricity of the ellipse x2sec2_...The eccentricity of an ellipse, with its centre at the origin, is . If one of the directrices is x = 4, then the equatio...The graph of the equation r2 = is a conic (where (r, θ) denotes the polar coordinates of the point) whose eccentric...