1
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

$$\triangle \mathrm{OAB}$$ is an equilateral triangle inscribed in the parabola $$\mathrm{y}^2=4 \mathrm{a} x, \mathrm{a}>0$$ with O as the vertex, then the length of the side of $$\triangle \mathrm{O A B}$$ is

A
$$8 \mathrm{a} \sqrt{3}$$ unit
B
8a unit
C
$$4 \mathrm{a} \sqrt{3}$$ unit
D
4a unit
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let A be the point (0, 4) in the xy-plane and let B be the point (2t, 0). Let L be the midpoint of AB and let the perpendicular bisector of AB meet the y-axis M. Let N be the midpoint of LM. Then locus of N is

A
a circle
B
a parabola
C
a straight line
D
a hyperbola
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let O be the vertex, Q be any point on the parabola x$$^2$$ = 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

A
$${x^2} = y$$
B
$${y^2} = x$$
C
$${y^2} = 2x$$
D
$${x^2} = 2y$$
4
WB JEE 2023
MCQ (Single Correct Answer)
+2
-0.5
Change Language

From the focus of the parabola $${y^2} = 12x$$, a ray of light is directed in a direction making an angle $${\tan ^{ - 1}}{3 \over 4}$$ with x-axis. Then the equation of the line along which the reflected ray leaves the parabola is

A
$$y = 2$$
B
$$y = 18$$
C
$$y = 9$$
D
$$y = 36$$
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