1
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1
Out of Syllabus

If the line $$y = 4 + kx,\,k > 0$$, is the tangent to the parabola $$y = x - {x^2}$$ at the point P and V is the vertex of the parabola, then the slope of the line through P and V is :

A
$${3 \over 2}$$
B
$${26 \over 9}$$
C
$${5 \over 2}$$
D
$${23 \over 6}$$
2
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1
Out of Syllabus

If $$y = {m_1}x + {c_1}$$ and $$y = {m_2}x + {c_2}$$, $${m_1} \ne {m_2}$$ are two common tangents of circle $${x^2} + {y^2} = 2$$ and parabola y2 = x, then the value of $$8|{m_1}{m_2}|$$ is equal to :

A
$$3 + 4\sqrt 2$$
B
$$- 5 + 6\sqrt 2$$
C
$$- 4 + 3\sqrt 2$$
D
$$7 + 6\sqrt 2$$
3
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1

Let $$x = 2t$$, $$y = {{{t^2}} \over 3}$$ be a conic. Let S be the focus and B be the point on the axis of the conic such that $$SA \bot BA$$, where A is any point on the conic. If k is the ordinate of the centroid of the $$\Delta$$SAB, then $$\mathop {\lim }\limits_{t \to 1} k$$ is equal to :

A
$${{17} \over {18}}$$
B
$${{19} \over {18}}$$
C
$${{11} \over {18}}$$
D
$${{13} \over {18}}$$
4
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

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 :

A
length of latus rectum 3
B
length of latus rectum 6
C
focus $$\left( {{4 \over 3},0} \right)$$
D
focus $$\left( {0,{3 \over 4}} \right)$$
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