1
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1

Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. Let e' and l' respectively be the eccentricity and length of the latus rectum of its conjugate hyperbola. If $${e^2} = {{11} \over {14}}l$$ and $${\left( {e'} \right)^2} = {{11} \over 8}l'$$, then the value of $$77a + 44b$$ is equal to :

A
100
B
110
C
120
D
130
2
JEE Main 2022 (Online) 28th June Evening Shift
+4
-1

If vertex of a parabola is (2, $$-$$1) and the equation of its directrix is 4x $$-$$ 3y = 21, then the length of its latus rectum is :

A
2
B
8
C
12
D
16
3
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

Let the eccentricity of the hyperbola $$H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ be $$\sqrt {{5 \over 2}}$$ and length of its latus rectum be $$6\sqrt 2$$. If $$y = 2x + c$$ is a tangent to the hyperbola H, then the value of c2 is equal to

A
18
B
20
C
24
D
32
4
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
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