1
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
Change Language
For the hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$, which of the following remains fixed when $$\alpha$$ varies?
A
directrix
B
vertices
C
foci
D
eccentricity
2
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The equation of the directrices of the hyperbola $$3{x^2} - 3{y^2} - 18x + 12y + 2 = 0$$ is
A
$$x = 3 \pm \sqrt {{{13} \over 6}} $$
B
$$x = 3 \pm \sqrt {{{6} \over 13}} $$
C
$$x = 6 \pm \sqrt {{{13} \over 3}} $$
D
$$x = 6 \pm \sqrt {{{3} \over 13}} $$
3
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then, the eccentricity e is
A
$$ = \sqrt 2 $$
B
$$ > \sqrt 2 $$
C
$$ < \sqrt 2 $$
D
$$ < {1 \over {\sqrt 2 }}$$
4
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
A point is in motion along a hyperbola $$y = {{10} \over x}$$ so that its abscissa x increases uniformly at a rate of 1 unit per second. Then, the rate of change of its ordinate when the point passes through (5, 2)
A
increases at the rate of $${1 \over 2}$$ unit per second
B
decreases at the rate of $${1 \over 2}$$ unit per second
C
decreases at the rate of $${2 \over 5}$$ unit per second
D
increases at the rate of $${2 \over 5}$$ unit per second
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