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Grade: 12

                        

Line 'L' has interceps a and b on the coordinate axis. When the axis are rotated through a given angle, keeping the origin fixed, the same line 'L' has intercepts p and q on the new axis, then A) a 2 + b 2 = p 2 + q 2 B) a 2 + p 2 = b 2 + q 2 C) 1/a 2 + 1/b 2 = 1/p 2 + 1/q 2 D) 1/a 2 + 1/p 2 = 1/b 2 + 1/q 2

11 years ago

Answers : (4)

Pratham Ashish
17 Points
							

hi,

 in the first coordinate sys,

x/a + y/b = 1     ..............................1

in other

x'/ p + y'/q  =1

where

 

\begin{align} x'&=x\cos\theta+y\sin\theta\\ y'&=-x\sin\theta+y\cos\theta. \end{align}

 

so,  x {  cos θ/p - sinθ /q }   + y { sinθ /p  + cosθ/ q }  =1 

comparing with (1).....

 {  cos θ/p - sinθ /q }/ 1/a   = { sinθ /p  + cosθ/ q }  / 1/b = 1/1

 cos θ/p - sinθ /q   = 1/a  ...............2

sinθ /p  + cosθ/ q  = 1/b ........................3

sq. and adding 2 &3

1/p^2 +  1/q^2  = 1/a^2 + 1/b^2

 

 

 

 

 

 

 

11 years ago
Aditya Lather
14 Points
							H
						
2 years ago
Aditya Lather
14 Points
							
Here the length of perpendicular from origin to the lines would be equal hence on equating that distance we get
√(1/p^2 +1/q^2)=√(1/a^2+1/b^2)
On squaring both sides we get the answer
2 years ago
Kushagra Madhukar
askIITians Faculty
605 Points
							
Dear student,
Please find the answer to your question.
 
Here the length of perpendicular from origin to the lines would be equal hence on equating that distance we get
√(1/p^2 +1/q^2)=√(1/a^2+1/b^2)
On squaring both sides we get the answer
Hence the correct option will be C
 
Thanks and regards,
Kushagra
2 months ago
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