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 Morning Shift
+4
-1
Out of Syllabus

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
3
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1
Out of Syllabus

The normal to the hyperbola

$${{{x^2}} \over {{a^2}}} - {{{y^2}} \over 9} = 1$$ at the point $$\left( {8,3\sqrt 3 } \right)$$ on it passes through the point :

A
$$\left( {15, - 2\sqrt 3 } \right)$$
B
$$\left( {9,2\sqrt 3 } \right)$$
C
$$\left( { - 1,9\sqrt 3 } \right)$$
D
$$\left( { - 1,6\sqrt 3 } \right)$$
4
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
Out of Syllabus
The point $$P\left( { - 2\sqrt 6 ,\sqrt 3 } \right)$$ lies on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ having eccentricity $${{\sqrt 5 } \over 2}$$. If the tangent and normal at P to the hyperbola intersect its conjugate axis at the point Q and R respectively, then QR is equal to :
A
$$4\sqrt 3$$
B
6
C
$$6\sqrt 3$$
D
$$3\sqrt 6$$
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