JEE Main 2021 (Online) 22th July Evening Shift | Conic Sections Question 92 | Mathematics

JEE Main 2021 (Online) 22th July Evening Shift

MCQ (Single Correct Answer)

-1

Let a line L : 2x + y = k, k > 0 be a tangent to the hyperbola x² $$-$$ y² = 3. If L is also a tangent to the parabola y² = $$\alpha$$x, then $$\alpha$$ is equal to :

$$-$$12

$$-$$24

JEE Main 2021 (Online) 22th July Evening Shift

MCQ (Single Correct Answer)

-1

Let $${E_1}:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1,a > b$$. Let E₂ be another ellipse such that it touches the end points of major axis of E₁ and the foci of E₂ are the end points of minor axis of E₁. If E₁ and E₂ have same eccentricities, then its value is :

$${{ - 1 + \sqrt 5 } \over 2}$$

$${{ - 1 + \sqrt 8 } \over 2}$$

$${{ - 1 + \sqrt 3 } \over 2}$$

$${{ - 1 + \sqrt 6 } \over 2}$$

JEE Main 2021 (Online) 20th July Evening Shift

MCQ (Single Correct Answer)

-1

Let P be a variable point on the parabola $$y = 4{x^2} + 1$$. Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x is :

$${(3x - y)^2} + (x - 3y) + 2 = 0$$

$$2{(3x - y)^2} + (x - 3y) + 2 = 0$$

$${(3x - y)^2} + 2(x - 3y) + 2 = 0$$

$$2{(x - 3y)^2} + (3x - y) + 2 = 0$$

JEE Main 2021 (Online) 20th July Morning Shift

MCQ (Single Correct Answer)

-1

Let the tangent to the parabola S : y² = 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle PQR is equal to :

$${{25} \over 2}$$

$${{35} \over 2}$$

$${{15} \over 2}$$

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