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

Question

The equation of tangent at the vertex of parabola x2+8x+4y=0 is (A) x=-4 (B) y=8 (C) y=4 (D) y=-8

Tardigrade Admin · Accepted Answer

Given, the equation of tangent x2+8x+4y=0 <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-kisqrgx6skwbrlgo.jpg" /> ⇒(x+4)2=-4(y-4) ⇒ X2=-4Y (by shifting the origin) X=x+4,Y=y-4 ∴ Vertex =(.-4,4.) Tangent at vertex is Y=0 y-4=0 or y=4

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

$x = - 4$

$y = 8$

$y = 4$

$y = - 8$

Given, the equation of tangent
$x^{2} + 8 x + 4 y = 0$

$\Rightarrow (x + 4)^{2} = - 4 (y - 4)$
$\Rightarrow X^{2} = - 4 Y$ (by shifting the origin)
$X = x + 4, Y = y - 4$
$∴$ Vertex $= (- 4, 4)$
Tangent at vertex is $Y = 0$
$y - 4 = 0$ or $y = 4$

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

x=−4

y=8

y=4

y=−8