JEE Main 2020 (Online) 4th September Morning Slot | Conic Sections Question 121 | Mathematics

JEE Main 2020 (Online) 4th September Morning Slot

MCQ (Single Correct Answer)

-1

Let P(3, 3) be a point on the hyperbola,
$${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal to it at P intersects the x-axis at (9, 0) and e is its eccentricity, then the ordered pair (a², e²) is equal to :

$$\left( {{9 \over 2},2} \right)$$

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

(9,3)

$$\left( {{9 \over 2},3} \right)$$

JEE Main 2020 (Online) 4th September Morning Slot

MCQ (Single Correct Answer)

-1

Let $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ (a > b) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function,
$$\phi \left( t \right) = {5 \over {12}} + t - {t^2}$$, then a² + b² is equal to

145

126

135

116

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)

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

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

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