Question

The equation of the tangent to the parabola $y = 3 x + 7$is

• A. $y - 3 x + 4 = 0$
• B. $3 y - x + 36 = 0$
• C. $3 y + x - 36 = 0$
• D. $3 y + x + 36 = 0$

Answer 1

Answer: (A)

$y - 3 x + 4 = 0$

Answer 2

A line perpendicular to the given line is $3 y + x = \lambda$

⇒ $y = - \frac { 1 } { 3 } x + \frac { \lambda } { 3 }$

Here $m = - \frac { 1 } { 3 }$ , $y ^ { 2 } = 16 x$ with $y ^ { 2 } = 4 a x$ then $a = 4$

Condition for tangency is $c = \frac { a } { m }$ ⇒$\frac { \lambda } { 3 } = \frac { 4 } { ( - 1 / 3 ) }$⇒ $\lambda = - 36$ .

∴ Required equation is $x + 3 y + 36 = 0$