Question

A circle S ≡ 0 passes through the common points of family of circles x² + y² + λx – 4y + 3 = 0(λ ∈ R) and have minimum area then

(a) area of S ≡ 0 is π sq. u

(b) radius of director circle of S ≡ 0 is √2

(c) Radius of director circle of S ≡ 0 for x–axis is 1 unit

(d) S ≡ 0 never cuts |2x| = 1

Answer 1

Correct option is (b) radius of director circle of S ≡ 0 is √2

for minimum area radius must be minimum

Since g² + 1 is positive so g must be zero

∴ radius = 1

Area = πr² = π sq. u.

Radius of director circle is √2 times the radius of the given circle.

∴ Radius of director circle is √2.