1
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
2
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let the eccentricity of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ be reciprocal to that of the ellipse x2 + 9y2 = 9, then the ratio of a2 : b2 equals to
A
8 : 1
B
1 : 8
C
9 : 1
D
1 : 9
3
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let P be a point on the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ and the line through P parallel to the Y-axis meets the circle x2 + y2 = 9 at Q, where P, Q are on the same side of the X-axis. If R is a point on PQ such that $${{PR} \over {RQ}} = {1 \over 2}$$, then the locus of R is
A
$${{{x^2}} \over 9} + {{9{y^2}} \over {49}} = 1$$
B
$${{{x^2}} \over {49}} + {{{y^2}} \over 9} = 1$$
C
$${{{x^2}} \over 9} + {{{y^2}} \over {49}} = 1$$
D
$${{9{x^2}} \over {49}} + {{{y^2}} \over 9} = 1$$
4
WB JEE 2017
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let P be the foot of the perpendicular from focus S of hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ on the line bx $$-$$ ay = 0 and let C be the centre of the hyperbola. Then, the area of the rectangle whose sides are equal to that of SP and CP is
A
2ab
B
ab
C
$${{({a^2} + {b^2})} \over 2}$$
D
$${a \over b}$$
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