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raman malik 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) a2 + b2 = p2 + q2


B) a2 + p2 = b2 + q2


C) 1/a2 + 1/b2 = 1/p2 + 1/q2


D) 1/a2 + 1/p2 = 1/b2 + 1/q2

7 years ago

Answers : (1)

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


 


 


 


 


 


 


 

7 years ago
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