24. The coordinate axes are rotated about the origin O in the
counterclockwise direction through an angle 60° If p and
q are the intercepts made on the new axes by a straight line
whose equation refered to the orginnal axes
x +y = 1 the 1/ p2 + 1/q2 =
Answers
Answered by
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Step-by-step explanation:
Let X and Y be the coordinates in the new coordinate system.
When axis are rotated through 60
∘
, co-ordinates are changed to
x=X(
2
1
)−Y(
2
3
)
y=X(
2
3
)+Y(
2
1
)
3x+4y=5
In the new coordinate system, the line will be represented as
3(X(
2
1
)−Y(
2
3
))+4(X(
2
3
)+Y(
2
1
))=5
X(3+4
3
)+Y(4−3
3
)=10
⇒a=
3+4
3
10
;b=
4−3
3
10
a
2
1
+
b
2
1
=
(10)
2
(3+4
3
)
2
+(4−3
3
)
2
=
100
25+75
=1
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