1
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

If the equation of the parabola, whose vertex is at (5, 4) and the directrix is $$3x + y - 29 = 0$$, is $${x^2} + a{y^2} + bxy + cx + dy + k = 0$$, then $$a + b + c + d + k$$ is equal to :

A
575
B
$$-$$575
C
576
D
$$-$$576
2
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1
Out of Syllabus

Let the normal at the point on the parabola y2 = 6x pass through the point (5, $$-$$8). If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is :

A
$$-$$3
B
$$-$$$${{9} \over 4}$$
C
$$-$$$${{5} \over 2}$$
D
$$-$$2
3
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
$${23 \over 6}$$
4
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
$$7 + 6\sqrt 2$$
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