The area (in square units) of the triangle formed by the lines 6 x^2+13 x y+6 y^2=0 and x+2 y+3=0 is

Step-by-step solution

Given the curve, 6 x^2+13 x y+6 y^2=0 Comparing with a x^2+2 h x y+b y^2=0 , we get a=6, b=6, h= 13 2 and a line x+2 y+3=0 comparing with l x+m y+n=0 , we get, l=1, m=2, n=3 So, required area = n^2 h^2-a b |a m^2-2 h l m+b l^2 | = 9 169 4 -36 |6 4-13 1 2+6 1| = 9 5 2 4 = 45 8 sq. units.