If the tangents on the ellipse 4x^{2} + y^{2} = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a^{2} is equal to 

(a) 

(b) 

(c) 

(d) 

If the tangents on the ellipse 4x^{2} + y^{2} = 8 at the points (1, 2) and (a, b) are perpendicular to each other, then a^{2} is equal to 

(a) 

(b) 

(c) 

(d) 

Equation of tangent at A(1, 2);
4x + 2y = 8 ⇒ 2x + y = 4
So tangent at B(a, b) can be assumed as
x − 2y = c ⇒ y =
Condition for tangency
⇒
Equation of tangent; x − 2y = ...(i)
Equation of tangent at P(a, b); 4ax + by = 8...(ii)
Comparing both the equations;
⇒ a = 2
⇒ a^{2} =