JEE Main 2020 (Online) 3rd September Evening Slot | Conic Sections Question 123 | Mathematics

JEE Main 2020 (Online) 3rd September Evening Slot

MCQ (Single Correct Answer)

-1

Let the latus ractum of the parabola y² = 4x be the common chord to the circles C₁ and C₂ each of them having radius 2$$\sqrt 5 $$. Then, the distance between the centres of the circles C₁ and C₂ is :

$$8\sqrt 5 $$

$$4\sqrt 5 $$

JEE Main 2020 (Online) 3rd September Evening Slot

MCQ (Single Correct Answer)

-1

Let e₁ and e₂ be the eccentricities of the ellipse,
$${{{x^2}} \over {25}} + {{{y^2}} \over {{b^2}}} = 1$$(b < 5) and the hyperbola,
$${{{x^2}} \over {16}} - {{{y^2}} \over {{b^2}}} = 1$$ respectively satisfying e₁e₂ = 1. If $$\alpha $$
and $$\beta $$ are the distances between the foci of the
ellipse and the foci of the hyperbola
respectively, then the ordered pair ($$\alpha $$, $$\beta $$) is equal to :

(8, 10)

(8, 12)

$$\left( {{{24} \over 5},10} \right)$$

$$\left( {{{20} \over 3},12} \right)$$

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 = $${1 \over 4}$$

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