Question

The line x sin θ – y cos θ = k touches the circle x2 + y2 = k2 then θ = ………

(a) θ ∈ [{(– 1)/2}, (1/2)]

(b) θ ∈ [0, 1]

(c) θ [– 1, 1]

(d) θ is any angle

Answer 1

The correct option (d) θ is any angle

Explanation:

y = mx + c touches the circle if c2 = a2(1 + m2)

given: y cos θ = x sin θ – k

∴ y = x tan θ – k secθ

hence c2 = k2 sec2θ

and a2(1 + m2) = k2(1 + tan2θ) ---------- a2 = k2

= k2 sec2θ

∴ c2 = a2(1 + m2)

⇒ θ is any angle as it is true for all values θ.