The equation of the parabola whose vertex and | vedclass

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

Question

(C) Given: Vertex $(h, k) = (0, 4)$ and focus $(0, 2)$.Since the $x$-coordinate of the vertex and focus are the same,the axis of the parabola is verti

Vedclass · Accepted Answer

$x^2 + 8y = 32$

Vedclass · Answer

(C) Given: Vertex $(h, k) = (0, 4)$ and focus $(0, 2)$.Since the $x$-coordinate of the vertex and focus are the same,the axis of the parabola is vertical.The distance between the vertex and the focus is $a = |4 - 2| = 2$.Since the focus is below the vertex,the parabola opens downwards.The standard equation for a downward-opening parabola is $(x - h)^2 = -4a(y - k)$.Substituting the values: $(x - 0)^2 = -4(2)(y - 4)$.$x^2 = -8(y - 4)$.$x^2 = -8y + 32$.$x^2 + 8y = 32$.

The equation of the parabola whose vertex and focus are $(0, 4)$ and $(0, 2)$ respectively,is

Similar Questions

What is the area of the triangle formed by the vertex of the parabola $x^2 = 12y$ and the endpoints of its latus rectum (in square units)?

An arch is in the form of a parabola with its axis vertical. The arch is $10 \, m$ high and $5 \, m$ wide at the base. How wide is it $2 \, m$ from the vertex of the parabola (in $, m$)?

Let $Z$ be the point of intersection of the axis and the directrix of the parabola $4x^2 - 12x + 4y + 5 = 0$. If $S$ is its focus,then the point which divides $SZ$ in the ratio $2:1$ is

The equation of the parabola with its vertex at the origin,axis on the $y$-axis and passing through the point $(6, -3)$ is

The area of a triangle (in sq. units) formed by the latus rectum of the parabola $x^2=16y$ and the lines joining the vertex of the parabola to the ends of the latus rectum is

Vedclass Test Series

Exam Paper Generator

Online Exam Module