Question

The equation of curve passing through (1, 1) in which the sub-tangent is always bisected at the origin is –

• A. y² = x
• B. 2x² – y² = 1
• C. x² + y² = 2
• D. x + y = 2

Answer 1

Answer: (A)

y² = x

Answer 2

TM is sub-tangent where T ≡ $\left( x - y \frac { d x } { d y } , 0 \right)$ and

M ≡ (x, 0)

$\frac { 1 } { 2 }$ $\left( x - y \frac { d x } { d y } + x \right)$= 0

⇒ 2x – y = 0 or 2 $\int \frac { d y } { y }$ = $\int \frac { \mathrm { dx } } { \mathrm { x } }$

2_­lny = lncx

y² = cx

curve passes through (1, 1)

∴ c = 1, y² = x