Question

If the length of subnormal is equal to length of subtangent at any point (3, 4) on the curve y = ƒ(x) and the tangent at (3, 4) to y = ­ƒ(x) meets the coordinate axes at A and B, then maximum area of the ∆OAB where O is origin, is –

• A. $\frac{45}{2}$
• B. $\frac{49}{2}$
• C. $\frac{25}{2}$
• D. $\frac{81}{2}$

Answer 1

Answer: (B)

$\frac{49}{2}$

Answer 2

Length of subnormal = length of subtangent

⇒  $\frac{dy}{dx}$ = ± 1

If $\frac{dy}{dx}$ = 1, equation of tangent is

y – 4 = x – 3 ⇒ y – x = 1

Area of ∆OAB = $\frac{1}{2}$ × 1 × 1 = $\frac{1}{2}$ … (i)

If $\frac{dy}{dx}$ = –1, equation of tangent is

y – 4 = – x + 3 ⇒ x + y = 7

Area of ∆OAB = $\frac{1}{2}$ × 7 × 7 = $\frac{49}{2}$ … (ii)

∴ Maximum area = $\frac{49}{2}$

Hence (2) is the correct answer.