JEE Main 2024 (Online) 6th April Morning Shift | Parabola Question 4 | Mathematics

Let $$C$$ be the circle of minimum area touching the parabola $$y=6-x^2$$ and the lines $$y=\sqrt{3}|x|$$. Then, which one of the following points lies on the circle $$C$$ ?

$$(1,2)$$

$$(2,2)$$

$$(1,1)$$

$$(2,4)$$

JEE Main 2024 (Online) 4th April Evening Shift

MCQ (Single Correct Answer)

-1

Let $$P Q$$ be a chord of the parabola $$y^2=12 x$$ and the midpoint of $$P Q$$ be at $$(4,1)$$. Then, which of the following point lies on the line passing through the points $$\mathrm{P}$$ and $$\mathrm{Q}$$ ?

$$(3,-3)$$

$$\left(\frac{1}{2},-20\right)$$

$$(2,-9)$$

$$\left(\frac{3}{2},-16\right)$$

JEE Main 2024 (Online) 27th January Morning Shift

MCQ (Single Correct Answer)

-1

If the shortest distance of the parabola $y^2=4 x$ from the centre of the circle $x^2+y^2-4 x-16 y+64=0$ is $\mathrm{d}$, then $\mathrm{d}^2$ is equal to :

JEE Main 2023 (Online) 13th April Morning Shift

MCQ (Single Correct Answer)

-1

Let $$\mathrm{PQ}$$ be a focal chord of the parabola $$y^{2}=36 x$$ of length 100 , making an acute angle with the positive $$x$$-axis. Let the ordinate of $$\mathrm{P}$$ be positive and $$\mathrm{M}$$ be the point on the line segment PQ such that PM : MQ = 3 : 1. Then which of the following points does NOT lie on the line passing through M and perpendicular to the line $$\mathrm{PQ}$$?

$$(6,29)$$

$$(-3,43)$$

$$(3,33)$$

$$(-6,45)$$

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