1
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
If a directrix of a hyperbola centred at the origin and passing through the point (4, –2$$\sqrt 3$$ ) is 5x = 4$$\sqrt 5$$ and its eccentricity is e, then :
A
4e4 – 24e2 + 27 = 0
B
4e4 – 24e2 + 35 = 0
C
4e4 – 12e2 - 27 = 0
D
4e4 + 8e2 - 35 = 0
2
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
If the line x – 2y = 12 is tangent to the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ at the point $$\left( {3, - {9 \over 2}} \right)$$ , then the length of the latus rectum of the ellipse is :
A
5
B
9
C
$$8\sqrt 3$$
D
$$12\sqrt 2$$
3
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
If the tangent to the parabola y2 = x at a point ($$\alpha$$, $$\beta$$), ($$\beta$$ > 0) is also a tangent to the ellipse, x2 + 2y2 = 1, then $$\alpha$$ is equal to :
A
$$\sqrt 2 + 1$$
B
$$\sqrt 2 - 1$$
C
$$2\sqrt 2 + 1$$
D
$$2\sqrt 2 - 1$$
4
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
The area (in sq. units) of the smaller of the two circles that touch the parabola, y2 = 4x at the point (1, 2) and the x-axis is :-
A
$$4\pi \left( {3 +\sqrt 2 } \right)$$
B
$$8\pi \left( {2 - \sqrt 2 } \right)$$
C
$$8\pi \left( {3 - 2\sqrt 2 } \right)$$
D
$$4\pi \left( {2 - \sqrt 2 } \right)$$
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