The line y=mx intersects the circle x2+y2−4x−4y=0 and x2+y2+6x−8y=0 at points A & B (points being other than the origin). The range of m such that the origin divides AB internally is
A
m>43 or m<−2
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B
m>−1
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C
−2<m<43
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D
−1<m<34
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Solution
The correct option is D−1<m<34
O divides AB internally in the ratio λ:1 λ>0 A(x1,y1),B(x2,y2),y=mx ⇒A(x1,mx1),B(x2,mx2) Section formula : (0,0)=(λx2+x1λ+1,λmx2+mx1λ+1) ⇒x1=−λx2 Or λ=−x1x2>0⇒x1x2<0