Examsnet
Unconfined exams practice
Home
Exams
Banking Entrance Exams
CUET Exam Papers
Defence Exams
Engineering Exams
Finance Entrance Exams
GATE Exam Practice
Insurance Exams
International Exams
JEE Exams
LAW Entrance Exams
MBA Entrance Exams
MCA Entrance Exams
Medical Entrance Exams
Other Entrance Exams
Police Exams
Public Service Commission (PSC)
RRB Entrance Exams
SSC Exams
State Govt Exams
Subjectwise Practice
Teacher Exams
SET Exams(State Eligibility Test)
UPSC Entrance Exams
Aptitude
Algebra and Higher Mathematics
Arithmetic
Commercial Mathematics
Data Based Mathematics
Geometry and Mensuration
Number System and Numeracy
Problem Solving
Board Exams
Andhra
Bihar
CBSE
Gujarat
Haryana
ICSE
Jammu and Kashmir
Karnataka
Kerala
Madhya Pradesh
Maharashtra
Odisha
Tamil Nadu
Telangana
Uttar Pradesh
English
Competitive English
Certifications
Technical
Cloud Tech Certifications
Security Tech Certifications
Management
IT Infrastructure
More
About
Careers
Contact Us
Our Apps
Privacy
Test Index
JEE Main Math Class 11 Coordinate Geometry Part 1 Questions
Show Para
Hide Para
Share question:
© examsnet.com
Question : 28
Total: 100
A stair-case of length
l
rests against a vertical wall and a floor of a room. Let
P
be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio 1: 2 . If the stair-case begins to slide on the floor, then the locus of P is:
[Online April 11, 2014]
an ellipse of eccentricity
1
2
an ellipse of eccentricity
√
3
2
a circle of radius
1
2
a circle of radius
√
3
2
l
Validate
Solution:
Let point
A
(
a
,
0
)
is on
x
-axis and
B
(
0
,
b
)
is on
y
-axis.
Let
P
(
h
,
k
)
divides
A
B
in the ratio 1: 2 . So, by section formula
h
=
2
(
0
)
+
1
(
a
)
1
+
2
=
a
3
k
=
2
(
b
)
+
1
(
0
)
3
=
2
b
3
⇒
a
=
3
h
and
b
=
3
k
2
Now,
a
2
+
b
2
=
l
2
⇒
9
h
2
+
9
k
2
4
=
l
2
⇒
h
2
(
l
3
)
2
+
k
2
(
2
l
3
)
2
=
1
Now
e
=
√
1
−
(
l
2
9
×
9
4
l
2
)
=
√
1
−
1
4
=
√
3
2
Thus, required locus of
P
is an ellipse with eccentricity
√
3
2
© examsnet.com
Go to Question:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Prev Question
Next Question
Examsnet