JEE Main 2022 (Online) 24th June Evening Shift | Parabola Question 53 | Mathematics

A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with :

length of latus rectum 3

length of latus rectum 6

focus $$\left( {{4 \over 3},0} \right)$$

focus $$\left( {0,{3 \over 4}} \right)$$

JEE Main 2022 (Online) 24th June Morning Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

Let x² + y² + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola y = x² at (2, 4). Then A + C is equal to ___________.

88/5

$$-$$8

JEE Main 2021 (Online) 1st September Evening Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

Consider the parabola with vertex $$\left( {{1 \over 2},{3 \over 4}} \right)$$ and the directrix $$y = {1 \over 2}$$. Let P be the point where the parabola meets the line $$x = - {1 \over 2}$$. If the normal to the parabola at P intersects the parabola again at the point Q, then (PQ)² is equal to :

$${{75} \over 8}$$

$${{125} \over {16}}$$

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

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

JEE Main 2021 (Online) 31st August Morning Shift

MCQ (Single Correct Answer)

-1

The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S (> R) respectively from the origin, is :

4(S + R)

2(S $$-$$ R)

4(S $$-$$ R)

2(S + R)

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