JEE Main 2020 (Online) 3rd September Morning Slot | Conic Sections Question 126 | Mathematics

JEE Main 2020 (Online) 3rd September Morning Slot

MCQ (Single Correct Answer)

-1

A hyperbola having the transverse axis of length $$\sqrt 2 $$ has the same foci as that of the ellipse 3x² + 4y² = 12, then this hyperbola does not pass through which of the following points ?

$$\left( {1, - {1 \over {\sqrt 2 }}} \right)$$

$$\left( {\sqrt {{3 \over 2}} ,{1 \over {\sqrt 2 }}} \right)$$

$$\left( { - \sqrt {{3 \over 2}} ,1} \right)$$

$$\left( {{1 \over {\sqrt 2 }},0} \right)$$

JEE Main 2020 (Online) 3rd September Morning Slot

MCQ (Single Correct Answer)

-1

Let P be a point on the parabola, y² = 12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is $${4 \over 3}$$, then :

MQ = $${1 \over 3}$$

PN = 4

PN = 3

MQ = $${1 \over 4}$$

JEE Main 2020 (Online) 2nd September Evening Slot

MCQ (Single Correct Answer)

-1

The area (in sq. units) of an equilateral triangle inscribed in the parabola y² = 8x, with one of its vertices on the vertex of this parabola, is :

$$256\sqrt 3 $$

$$64\sqrt 3 $$

$$128\sqrt 3 $$

$$192\sqrt 3 $$

JEE Main 2020 (Online) 2nd September Evening Slot

MCQ (Single Correct Answer)

-1

For some $$\theta \in \left( {0,{\pi \over 2}} \right)$$, if the eccentricity of the
hyperbola, x²–y²sec²$$\theta $$ = 10 is $$\sqrt 5 $$ times the
eccentricity of the ellipse, x²sec²$$\theta $$ + y² = 5, then the length of the latus rectum of the ellipse, is:

$$\sqrt {30} $$

$$2\sqrt 6 $$

$${{4\sqrt 5 } \over 3}$$

$${{2\sqrt 5 } \over 3}$$

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