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KVPY SX SB Exam 19-Nov-2017 Question Paper
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© examsnet.com
Question : 1
Total: 120
Consider a rigid square ABCD as in the figure with A and B on the x and y axis respectively.
When A and B slide along their respectiveaxes, the locus of C forms a part of
a circle
a parabola
a hyperbola
an ellipse which is not a circle
Validate
Solution:
C(h, k)
h
=
a
sin
θ
⇒
sin
θ
=
h
a
k = a sinθ + a cos θ
k = h + a cos θ
k
−
h
a
=
cos
θ
....(2)
sin
2
θ
+
cos
2
θ
=
1
h
2
a
2
+
(
k
−
h
)
2
a
2
=
1
h
2
+
(
k
−
h
)
2
=
a
2
locus
x
2
+
(
y
−
x
)
2
=
a
2
solving we get
x
2
+
y
2
+
x
2
−
2
x
y
=
a
2
2
x
2
+
y
2
−
2
x
y
=
a
2
check
h
2
−
a
b
<
0
ellipse
© examsnet.com
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