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let L1 be a straight line through the origin and L2 be the straight line x+y=1.if the intercept made by the circle x²+y²-x+3y=0 on L1 and L2 are equal, then which of the following represents L1? one answer is x-y=0 that answer i have got but how to get second answer that is x-7y=0

let L1 be a straight line through the origin and L2 be the straight line x+y=1.if the intercept made by the circle x²+y²-x+3y=0 on L1 and L2 are equal, then which of the following represents L1? one answer is x-y=0 that answer i have got but how to get second answer that is x-7y=0

Grade:11

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
6 years ago
It’s simple
Lets say L1 is y=mx
Then as chords are equal the perpendicular distance from the center of the circle should also be same
center is
(1/2,-3/2)
so we have (by equating the perpendicular distance from center to L1 and L2)
\frac{|m/2+3/2|}{\sqrt{m^2+1}} = \frac{|1/2-3/2-1|}{\sqrt{2}} = \sqrt{2}
squaring and simplifying we get the quadratic as
7m^2+6m -1=0
whose roots are
m=1,-1/7
so possible values of L1 are
x=y and
x = -7y

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