If  Aand B  are two points on the line 12x+5y+65=0, such that OA=OB=13 then the area of the triangle is

The perpendicular distance from a point Px1,y1 to the line ax+by+c=0 is ax1+by1+ca2+b2 The perpendicular distance from a point (0,0) to the line 12x+5y+65=0 is 120+50+65144+25=6513=5 Consider the triangle, Use Pythagorean Theorem to get the length of the base as 12+12=24 Hence the area of the triangle is 12(24)(5)=60 sq units