Question
Question: If the tangent to the ellipse x<sup>2</sup> + 4y<sup>2</sup> = 16 at the point P(θ) is a normal to t...
If the tangent to the ellipse x2 + 4y2 = 16 at the point P(θ) is a normal to the circle x2 + y2 - 8x - 4y = 0, then θ equals
A
π/2
B
π/4
C
0
D
- π/4
Answer
π/2
Explanation
Solution
P(θ) on the circle x2 + 4y2 = 16 is (4 cosθ, 2 sinθ)
Equation of tangent at P is
4 cosθ x + 8 sinθ y = 16
⇒ cos θx + 2 sin θy = 4.
Since, it passes through centre (4, 2) of given circle, therefore
∴ 4 cosθ + 4 sinθ = 4
⇒ cosθ + sinθ = 1, θ = 0, 2π.