Question

If the line joining the points (0, 3) and (5, −2) is a tangent to the curve y = then

• A. a = 1 ± $\sqrt{3}$
• B. a = φ
• C. a = −1 ± $\sqrt{3}$
• D. a = -2 ± 2$\sqrt{3}$

Answer 1

Answer: (B)

a = φ

Answer 2

Equation of line joining the points (0, 3) and (5, −2) is

y = 3 − x. If line is a tangent to y = then (3 − x) (x +1)

= ax should have equal roots. Thus (a − 2)² + 12 = 0 ⇒ a = φ.