1
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

The equations of two sides of a variable triangle are $$x=0$$ and $$y=3$$, and its third side is a tangent to the parabola $$y^2=6x$$. The locus of its circumcentre is :

A
$$4{y^2} - 18y - 3x - 18 = 0$$
B
$$4{y^2} + 18y + 3x + 18 = 0$$
C
$$4{y^2} - 18y + 3x + 18 = 0$$
D
$$4{y^2} - 18y - 3x + 18 = 0$$
2
JEE Main 2023 (Online) 25th January Morning Shift
+4
-1
Out of Syllabus

The distance of the point $$(6,-2\sqrt2)$$ from the common tangent $$\mathrm{y=mx+c,m > 0}$$, of the curves $$x=2y^2$$ and $$x=1+y^2$$ is :

A
$$\frac{1}{3}$$
B
5
C
$$\frac{14}{3}$$
D
5$$\sqrt3$$
3
JEE Main 2023 (Online) 24th January Evening Shift
+4
-1
Out of Syllabus

The equations of the sides AB and AC of a triangle ABC are $$(\lambda+1)x+\lambda y=4$$ and $$\lambda x+(1-\lambda)y+\lambda=0$$ respectively. Its vertex A is on the y-axis and its orthocentre is (1, 2). The length of the tangent from the point C to the part of the parabola $$y^2=6x$$ in the first quadrant is :

A
4
B
2$$\sqrt2$$
C
2
D
$$\sqrt6$$
4
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1
Out of Syllabus

Let a tangent to the curve $$\mathrm{y^2=24x}$$ meet the curve $$xy = 2$$ at the points A and B. Then the mid points of such line segments AB lie on a parabola with the :

A
length of latus rectum 2
B
directrix 4x = $$-$$3
C
directrix 4x = 3
D
length of latus rectum $$\frac{3}{2}$$
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