If the angle between the pair of straight lines formed by joining the points of intersection of x2+y2=4 and y=3x+c to the origin is right angle, then c2=
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Solution
x2+y2=4→(1) y−3xc=1→(2) Required pair of straight lines can be obtained by homogenisation of curve (1) using line (2) ⇒x2+y2=4(y−3xc)2⇒(c2−36)x2+(c2−4)y2+24xy=0 ∵ Lines are perpendicular, ⇒c2−36+c2−4=0∴c2=20