450
900
600
0
Equation of any tangent to the ellipse x²/a² + y²/b² = 1 is xa cos θ + yb sin θ = 1.. (1)
Also, xa + yb = √2 (2) touches the given ellipse.
Comparing coefficients in (1) and (2), we get
(cos θ)/a = 1/√2 = (sin θ)/b = 1/√2
∴ cos θ = 1/√2 = sin θ
⇒ θ = 45°
Hence, option A.