What is the equation of the directrix of the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given equation: $y^2 + 4y + 4x + 2 = 0$Completing the square for $y$: $(y^2 + 4y + 4) - 4 + 4x + 2 = 0$$(y + 2)^2 = -4x + 2$$(y + 2)^2 = -4(x - \f

Vedclass · Accepted Answer

$x = \frac{3}{2}$

Vedclass · Answer

(D) Given equation: $y^2 + 4y + 4x + 2 = 0$Completing the square for $y$: $(y^2 + 4y + 4) - 4 + 4x + 2 = 0$$(y + 2)^2 = -4x + 2$$(y + 2)^2 = -4(x - \frac{1}{2})$Comparing this with the standard form $(Y)^2 = -4a(X)$,where $Y = y + 2$,$X = x - \frac{1}{2}$,and $4a = 4 \Rightarrow a = 1$.The vertex is $(\frac{1}{2}, -2)$.The equation of the directrix for $Y^2 = -4aX$ is $X = a$.Substituting the values: $x - \frac{1}{2} = 1$$x = 1 + \frac{1}{2} = \frac{3}{2}$.

What is the equation of the directrix of the parabola $y^2 + 4y + 4x + 2 = 0$?

Similar Questions

The locus of the poles of focal chords of the parabola $y^2 = 4ax$ is

Let the tangent to the curve $x^2+2x-4y+9=0$ at the point $P(1,3)$ on it meet the $y$-axis at $A$. Let the line passing through $P$ and parallel to the line $x-3y=6$ meet the parabola $y^2=4x$ at $B$. If $B$ lies on the line $2x-3y=8$,then $(AB)^2$ is equal to $............$.

Which one of the following equations,represented parametrically,represents a parabolic profile?

If $y=mx+1$ is a tangent to the parabola $y^2=4x$,then $m=$

Let $P(\alpha, \beta)$ be a point on the parabola $y^2 = 4x$. If $P$ also lies on the chord of the parabola $x^2 = 8y$ whose midpoint is $(1, 5/4)$,then $(\alpha - 28)(\beta - 8)$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module