Question

The parabola y² = 4x and the circle (x – 6)² + y² = r² will have no common tangent, if ‘r’ is equal to-

• A. r>$\sqrt{20}$
• B. r <$\sqrt{20}$
• C. r>$\sqrt{18}$
• D. r Ī ($\sqrt{20}$,$\sqrt{28}$)

Answer 1

Answer: (B)

r <$\sqrt{20}$

Answer 2

Any normal of parabola is y = –tx + 2t + t³. If it pass through (6, 0), then, –6t + 2t + t³ = 0

Ž t = 0, t² = 4

Thus A ŗ (4, 4)

Thus, for no common tangent,

AC > $\sqrt{4 + 16}$ > r Ž r < $\sqrt{20}$.