Question

The equation of the tangent to the parabola at point $\left( a / t ^ { 2 } , 2 a / t \right)$is

• A. $t y = x t ^ { 2 } + a$
• B. $t y = x + a t ^ { 2 }$
• C. $y = t x + a t ^ { 2 }$
• D. $y = t x + \left( a / t ^ { 2 } \right)$

Answer 1

Answer: (A)

$t y = x t ^ { 2 } + a$

Answer 2

Equation of the tangent to the parabola, $y ^ { 2 } = 4 a x$ is

$y y _ { 1 } = 2 a \left( x + x _ { 1 } \right)$

⇒ $y \cdot \frac { 2 a } { t } = 2 a \left( x + \frac { a } { t ^ { 2 } } \right)$ ⇒ $\frac { y } { t } = \left( x + \frac { a } { t ^ { 2 } } \right)$ ⇒ $\frac { y } { t } = \frac { t ^ { 2 } x + a } { t ^ { 2 } }$

⇒ $t y = t ^ { 2 } x + a$