6i think nishant sir did this one in that lecture of his didnt he?
not a doubt...
Prove that the straight lines joining the origin to the points of intersection of the straight lines hx+ky=2hk and the curve (x-k)2+(y-h)2=c2 are at right angles if h2+k2=c2
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6 Answers
6
49right! :)
the concept was "Homonzation"!!(don't know if the spelling is right or wrong!)
6naaa the spell is wrong!!
koi baat nahi we are students of HSMS...dont expect us to good in spells...:P:P
its easy ...
1A few good observations reduce this problem to a sitter !
The given straight line : - h x + k y = 2 h k
The given circle : - ( x - k ) 2 + ( y - h ) 2 = c 2
Observations : -
1 . The given straight line passes through the center of the circle .
2 . This indicates that the given line is , in fact , " a diameter " of the given circle .
3 . Since the lines joining Origin to the point of intersection of the line and the circle are at right angles , hence , Origin must lie on the cirle , so that the line ( which is proven to be a diameter ) and Origin are parts of a semicircle .
4 . Now that we know origin lies on the circle , let us put " ( 0 , 0 ) " in the equation of the circle .
Voila !!!!!!!!!!!!!! Eureka !!!!!!!!!!!!!!
h 2 + k 2 = c 2