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Let L1 be a straight linepassing through origin and L2 be a straight line x+y=1. If intercepts made by the circle x^2 + y^2 – x + 3y=0 on L1 and L2 are equal then which of the following equations can represent L1? a)x+y=0 b)y-x=0 c)y+7x=0 d)x-7y=0

Let L1 be a straight linepassing through origin and L2 be a straight line x+y=1. If intercepts made by the circle x^2 + y^2 – x + 3y=0 on L1 and L2 are equal then which of the following equations can represent L1?
a)x+y=0      b)y-x=0      c)y+7x=0       d)x-7y=0

Grade:12th pass

1 Answers

Arun
25750 Points
5 years ago
whose roots arem=1,-1/7so possible values of L1 arex=y andx = -7y7m^2+6m -1=0squaring and simplifying we get the quadratic as\frac{|m/2+3/2|}{\sqrt{m^2+1}} = \frac{|1/2-3/2-1|}{\sqrt{2}} = \sqrt{2}It’s simpleLets say L1 is y=mxThen as chords are equal the perpendicular distance from the center of the circle should also be samecenter is(1/2,-3/2)so we have (by equating the perpendicular distance from center to L1 and L2)
 
 
Regards
Arun

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