Question

If x + y = a be a tangent to the ellipse x²/9 + y²/16= 1, then find the value of (|a| + 1).

Answer 1

The line y = mx + c, will be a tangent to the

ellipse x²/a² + y²/b² = 1, then c² = a² m² + b²

Here, c = a, m = –1, a² = 9, b² = 16

Thus, a² = 16 + 9 = 25

⇒ a = ± 5

⇒ (|a| + 1) = |± 5| + 1 = 6