Questions
The coordinates of the middle point of the chord intercepted on line by the circle are
a
−ll2+m2,−ml2+m2
b
−ln12+m2,−mnl2+m2
c
−lnl2+m2,−mnl2+m2
d
none of these
detailed solution
Correct option is B
Let x1,y1 be the mid-point of the chord intercepted by the circle x2+y2=a2 on the line lx+my+n=0.Then, the equation of the chord of the circle x2+y2=a2whose middle point is x1,y1 isxx1+yy1−a2=x12+y12a2⇒xx1+yy1=x12+y12Clearly, lx+my+n=0 and (i) represents the same line. ∴ x1l=y1m=−x12+y12n=λ, say ⇒ x1=lλ,y1=mλ and x12+y12=−nλ⇒ l2+m2λ2=−nλ⇒ λ=−nl2+m2∴ x1=−lnl2+m2,y1=mnl2+m2Hence, the required points is −ml2+m2,−mnl2+m2Talk to our academic expert!
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