1
JEE Main 2019 (Online) 12th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
If the normal to the ellipse 3x2 + 4y2 = 12 at a point P on it is parallel to the line, 2x + y = 4 and the tangent to the ellipse at P passes through Q(4,4) then PQ is equal to :
A
$${{\sqrt {61} } \over 2}$$
B
$${{\sqrt {221} } \over 2}$$
C
$${{\sqrt {157} } \over 2}$$
D
$${{5\sqrt 5 } \over 2}$$
2
JEE Main 2019 (Online) 10th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The tangent and normal to the ellipse 3x2 + 5y2 = 32 at the point P(2, 2) meet the x-axis at Q and R, respectively. Then the area (in sq. units) of the triangle PQR is :
A
$${{14} \over 3}$$
B
$${{16} \over 3}$$
C
$${{68} \over {15}}$$
D
$${{34} \over {15}}$$
3
JEE Main 2019 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
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
$$12\sqrt 2 $$
4
JEE Main 2019 (Online) 9th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
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
$$2\sqrt 2 - 1$$
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