The angle between the tangents drawn from the point (1,2) to the ellipse 3 x^2+2 y^2=5 is

Step-by-step solution

Given Ellipse, 3 x^2+2 y^2-5=0 Then, equations of pairs of tangents drawn to the ellipse S from the point (1,2) . aligned & S S₁=T^2 & (3 x^2+2 y^2-5 ) (3(1)^2-2(2)^2-5 ) & =(3 x(1)+2 y(2)-5)^2 & (3 x^2+2 y^2-5 )(6)=(3 x+4 y-5)^2 & 18 x^2+12 y^2-30=9 x^2+16 y^2+25 & +24 x y-40 y-30 aligned 9 x^2-4 y^2-24 x y+30 x+40 y-55=0 Now, the angle between these lines is given by aligned & = 2 h^2-a b a+b & = 2 144+36 5 = 2 180 5 = 12 5 5 & = ⁻¹ ( 12 5 5 ) aligned