If the line 3x-4y= k cuts the circle x2+y2-4x-8y-5=0 in two points then the limits of k are

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We have,3x-4y=k3x-4y-k=0x2+y2-4x-8y-5=0Center of circle x2+y2+2gx+2fy+c=0 is -g,-fHence center of given circle=2,4Radius=g2+f2-c=22+42--5=4+16+5=5 unitsIf line intersects circle at two points then length of perpendicular from center of circle must beless than radius of circle.3.2-4.4-k32+42<56-16-k5<5-k+10<25k+10<25ifx<a, then-a<x<a-25<k+10<25-25-10<k+10-10<25-10-35<k<15 Answer

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