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  4. The equation of tangent at the vertex of parabola x2+8x+4y=0 is

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Q. The equation of tangent at the vertex of parabola $x^{2}+8x+4y=0$ is

NTA AbhyasNTA Abhyas 2022

Solution:

Given, the equation of tangent
$x^{2}+8x+4y=0$
Solution
$\Rightarrow(x+4)^2=-4(y-4)$
$\Rightarrow X^{2}=-4Y$ (by shifting the origin)
$X=x+4,Y=y-4$
$\therefore $ Vertex $=\left(\right.-4,4\left.\right)$
Tangent at vertex is $Y=0$
$y-4=0$ or $y=4$