If the line x-2y=m (m ∈Z ) intersects the circle x^2+y^2=2x+4y at two distinct points, then the number of possible values of m are

Question

Accepted Answer

Correct answer: B. (b) : Equation of circle is x^2+y^2=2x+4y, can be written as (x-1 )^2+ (y-2 )^2=5 ∴ Centre of circle is (1 ,2 ) and radius is 5. Distance of (1 ,2 ) from line x-2y-m=0 = ( 1-4-m 1^2+2^2 )< 5 (as line intersect the circle) ⇒ |-3-m |<5 ⇒ |- (m+3 ) |<5 ⇒m+3<5 m=-7 ,-6 ,-5 ,-4 ,-3 ,-2 ,-1 ,0 ,1. ∴ Number of possible values of m is 9 .

$If the line x - 2 y = m (m \in Z) intersects the circle x^{2} + y^{2} = 2 x + 4 y at two distinct points, then the number of possible values of m are$

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