JEE Main 2021 (Online) 18th March Evening Shift | Hyperbola Question 41 | Mathematics

Consider a hyperbola H : x² $$-$$ 2y² = 4. Let the tangent at a
point P(4, $${\sqrt 6 }$$) meet the x-axis at Q and latus rectum at R(x₁, y₁), x₁ > 0. If F is a focus of H which is nearer to the point P, then the area of $$\Delta$$QFR is equal to :

$${\sqrt 6 }$$ $$-$$ 1

$${7 \over {\sqrt 6 }}$$ $$-$$ 2

$${4\sqrt 6 }$$ $$-$$ 1

$${4\sqrt 6 }$$

JEE Main 2021 (Online) 16th March Morning Shift

MCQ (Single Correct Answer)

-1

The locus of the midpoints of the chord of the circle, x² + y² = 25 which is tangent to the hyperbola, $${{{x^2}} \over 9} - {{{y^2}} \over {16}} = 1$$ is :

(x² + y²)² $$-$$ 9x² + 16y² = 0

(x² + y²)² $$-$$ 9x² + 144y² = 0

(x² + y²)² $$-$$ 16x² + 9y² = 0

(x² + y²)² $$-$$ 9x² $$-$$ 16y² = 0

JEE Main 2021 (Online) 25th February Evening Shift

MCQ (Single Correct Answer)

-1

A hyperbola passes through the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is :

$${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$

$${{{x^2}} \over 9} - {{{y^2}} \over 16} = 1$$

$${{{x^2}} \over 9} - {{{y^2}} \over 25} = 1$$

x² $$-$$ y² = 9

JEE Main 2020 (Online) 5th September Evening Slot

MCQ (Single Correct Answer)

-1

Out of Syllabus

If the line y = mx + c is a common tangent to the hyperbola
$${{{x^2}} \over {100}} - {{{y^2}} \over {64}} = 1$$ and the circle x² + y² = 36, then which one of the following is true?

5m = 4

8m + 5 = 0

c² = 369

4c² = 369

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