JEE Main2010MathematicsCircleActual

The circle x^2+y^2=4 x+8 y+5 intersects the line 3 x-4 y=m at two distinct points if

Options

A-35 < m < 15
B15 < m < 65
C35 < m < 85
D-85 < m < -35

Correct answer

A. -35 < m < 15

Step-by-step solution

Circle x^2+y^2-4 x-8 y-5=0 Centre =(2,4) , Radius = 4+16+5 =5 If circle is intersecting line 3 x-4 y=m at two distinct points. length of perpendicular from centre < radius |6-16- m | 5 < 5 |10+ m | < 25 -25 < m+10 < 25 -35 < m < 15 .

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