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NIMCET 2012 Question Paper with solutions
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© examsnet.com
Question : 17
Total: 120
The equation of the ellipse with major axis along the x-axis and passing through the points (4, 3) and (- 1, 4) is
15
x
2
+
7
y
2
= 247
7
x
2
+
15
y
2
= 247
16
x
2
+
9
y
2
= 247
9
x
2
+
16
y
2
= 247
Validate
Solution:
The equation of an ellipse whose major axis along x-axis is
x
2
a
2
+
y
2
b
2
= 1 ... (i)
Eq, (i) passes through the points (4,3) and (-1,4) , then
16
a
2
+
9
b
2
= 1 ... (ii)
and
1
a
2
+
16
b
2
= 1 ... (iii)
From Eqs. (ii) and (iii),
16
(
1
−
16
b
2
)
+
9
b
2
= 1
⇒
9
b
2
−
256
b
2
= = 1 - 16
⇒
247
b
2
= 15
∴
b
2
=
247
15
From Eq. (iii)
1
a
2
= 1 -
16
b
2
= 1 -
15
247
× 16
⇒
1
a
2
=
247
−
240
247
=
7
247
⇒
(
a
2
=
247
7
)
Now, put the value of
a
2
and
b
2
in Eq. (i) and get the required equation of an ellipse
7
x
2
247
+
15
y
2
247
= 1
⇒
7
x
2
+
15
y
2
= 247
© examsnet.com
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