JEE Main 2019 (Online) 12th April Evening Slot | Ellipse Question 58 | Mathematics

If the normal to the ellipse 3x² + 4y² = 12 at a point P on it is parallel to the line, 2x + y = 4 and the tangent to the ellipse at P passes through Q(4,4) then PQ is equal to :

$${{\sqrt {61} } \over 2}$$

$${{\sqrt {221} } \over 2}$$

$${{\sqrt {157} } \over 2}$$

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

JEE Main 2019 (Online) 10th April Evening Slot

MCQ (Single Correct Answer)

-1

Out of Syllabus

The tangent and normal to the ellipse 3x² + 5y² = 32 at the point P(2, 2) meet the x-axis at Q and R, respectively. Then the area (in sq. units) of the triangle PQR is :

$${{14} \over 3}$$

$${{16} \over 3}$$

$${{68} \over {15}}$$

$${{34} \over {15}}$$

JEE Main 2019 (Online) 10th April Morning Slot

MCQ (Single Correct Answer)

-1

Out of Syllabus

If the line x – 2y = 12 is tangent to the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ at the point $$\left( {3, - {9 \over 2}} \right)$$ , then the length of the latus rectum of the ellipse is :

$$8\sqrt 3 $$

$$12\sqrt 2 $$

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