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KVPY SX SB Exam 2015 Question Paper
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© examsnet.com
Question : 83
Total: 120
A mirror in the first quadrant is in the shape of a hyperbola whose equation is
x
y
=
1
. A light source in the second quadrant emits a beam of light that hits the mirror at the point
(
2
,
1
2
)
. If the reflected ray is parallel to the y-axis, the slope of the incident beam is -
13
8
7
4
15
8
2
Validate
Solution:
Curve
y
=
1
x
d
y
d
x
=
−
1
x
2
slope of tangent =
−
1
4
at
(
2
,
1
2
)
slope of normal = 4
where foot of normal is
(
2
,
1
2
)
let slope at incident beam is 'm'
|
4
−
m
1
+
4
m
|
=
|
4
−
∞
1
+
4.
∞
|
4
−
m
1
+
4
m
=
±
1
4
m
=
15
8
© examsnet.com
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