Question

If the parabola $y^2 = 4ax$ passes through the point $(1, -2)$, then the tangent at this point is

• A. $x + y- 1 = 0$
• B. $x-y-1 = 0$
• C. $x + y + 1 = 0$
• D. $x-y- 1=0$

Answer 1

Answer: (C)

$x + y + 1 = 0$

Answer 2

Since the parabola $y^2 = 4ax$ passes through the point $(1, -2)$,
$\therefore \left(-2\right)^{2} = 4a\left(I\right) \Rightarrow a = 1$
Equation of tangent to the parabola at $\left(1,-2\right)$
$yy_{1} =2a\left(x + x_{1}\right)$ or
$y\left(-2\right) = 2\left(1\right)\left(x+1\right)$ or $x + y+1 = 0$