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AP EAMCET Engineering 21 Apr 2019 Shift 2 Paper
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© examsnet.com
Question : 43
Total: 160
If the equation of a curve C is transformed to
9
x
2
+
25
y
2
= 225 bu=y the rotation of the coordinate axes about the origin through an angle
π
4
in the positive direction then the equation of the curve C. , before the transformation is
17
x
2
+ 16xy +
17
y
2
= 225
17
x
2
+
23
y
2
= 391
17
x
2
- 16xy +
17
y
2
= 225
23
x
2
+
17
y
2
= 391
Validate
Solution:
The original and new coordinates are,
x
=
x
cos
π
4
−
y
sin
π
4
=
x
√
2
−
y
√
2
y
=
x
sin
π
4
+
y
cos
π
4
=
x
√
2
+
y
√
2
The equation of the curve is,
9
x
2
+
25
y
2
=
225
9
(
x
−
y
√
2
)
2
+
25
(
x
+
y
√
2
)
2
=
225
After simplification
9
x
2
+
9
y
2
+
18
x
y
+
25
x
2
+
25
y
2
−
50
x
y
=
450
34
x
2
+
34
y
2
−
32
x
y
=
450
17
x
2
+
17
y
2
−
16
x
y
=
225
© examsnet.com
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