Question

If y = 2x – 3 is a tangent to the parabola y² = 4a$\left( x - \frac{1}{3} \right)$, then a is equal to-

• A. 1
• B. – 1
• C. 14/3
• D. –14/3

Answer 1

Answer: (D)

–14/3

Answer 2

y = 2x – 3 ; y² = 4a(x – $\frac{1}{3}$)

y = 2 (x – $\frac{1}{3}$) + $\frac{a}{2}$ ̃ y = 2x –$\frac{2}{3}$ + $\frac{a}{2}$

$\frac{- 2}{3}$ + $\frac{a}{2}$ = –3 ̃ $\frac{a}{2}$ = – 3 + $\frac{2}{3}$

$\frac{a}{2}$ = $\frac{- 7}{3}$ ̃ a = $\frac{- 14}{3}$