JEE Main 2019 (Online) 11th January Evening Slot | Parabola Question 96 | Mathematics

If the area of the triangle whose one vertex is at the vertex of the parabola, y² + 4(x – a²) = 0 and the othertwo vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of 'a' is :

$$5\sqrt 5 $$

$${\left( {10} \right)^{2/3}}$$

$$5\left( {{2^{1/3}}} \right)$$

JEE Main 2019 (Online) 10th January Evening Slot

MCQ (Single Correct Answer)

-1

The length of the chord of the parabola x² $$=$$ 4y having equation x – $$\sqrt 2 y + 4\sqrt 2 = 0$$ is -

$$8\sqrt 2 $$

$$6\sqrt 3 $$

$$3\sqrt 2 $$

$$2\sqrt {11} $$

JEE Main 2019 (Online) 10th January Morning Slot

MCQ (Single Correct Answer)

-1

Out of Syllabus

If the parabolas y² = 4b(x – c) and y² = 8ax have a common normal, then which on of the following is a valid choice for the ordered triad (a, b, c)?

(1, 1, 3)

(1, 1, 0)

$$\left( {{1 \over 2},2,0} \right)$$

$$\left( {{1 \over 2},2,3} \right)$$

JEE Main 2019 (Online) 9th January Evening Slot

MCQ (Single Correct Answer)

-1

Let A(4, $$-$$ 4) and B(9, 6) be points on the parabola, y² = 4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of $$\Delta $$ACB is maximum. Then, the area (in sq. units) of $$\Delta $$ACB, is :

$$31{1 \over 4}$$

$$30{1 \over 2}$$

$$31{3 \over 4}$$

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