Question

If $y=2$ be the directrix and $(0,1)$ be the vertex of the parabola $x^2+\lambda y+\mu =0$ then $(\lambda ,\mu )$ is equal to

• A. $(8,-8)$
• B. $(8,8)$
• C. $(-4,4)$
• D. $(4,-4)$

Answer 1

Answer: (D)

$(4,-4)$

We know parabola passes through its vertex
$\Rightarrow 0+\lambda +\mu =0\Rightarrow \lambda +\mu =0$ ...... $\left(i\right)$
Now parabola is, $x^2+\lambda y+\mu =0$
$\Rightarrow x^2=-\lambda (y-1)$ ........... [Using $\left(i\right)$]
Thus directrix of this parabola is $y=1+\frac{\lambda }{4}=2$ ......... (given)
$\Rightarrow \lambda =4$

$\therefore \mu =-4$
Hence ordered pair is $(4,-4)$