If the vertex of a parabola is (0, a) and the | vedclass

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

Question

(B) The vertex of the parabola is $V(0, a)$ and the focus is $S(0, 0)$.Since the focus and vertex lie on the $y$-axis,the axis of the parabola is the

Vedclass · Accepted Answer

$x^2 = 4a(a - y)$

Vedclass · Answer

(B) The vertex of the parabola is $V(0, a)$ and the focus is $S(0, 0)$.Since the focus and vertex lie on the $y$-axis,the axis of the parabola is the $y$-axis.The distance between the vertex and the focus is $a = |a - 0| = |a|$.Since the focus is below the vertex,the parabola opens downwards.The standard form for a downward-opening parabola with vertex $(h, k)$ is $(x - h)^2 = -4a(y - k)$.Here,$(h, k) = (0, a)$ and the distance from vertex to focus is $a$.Substituting these values,we get $(x - 0)^2 = -4a(y - a)$.$x^2 = -4a(y - a)$.$x^2 = 4a(a - y)$.

If the vertex of a parabola is $(0, a)$ and the focus is $(0, 0)$,what is its equation?

Similar Questions

From a point $(d, 0)$, three normals are drawn to the parabola $y^{2} = x$. Then:

The equation of the tangent to the parabola $y = (x - 3)^2$ parallel to the chord joining the points $(3, 0)$ and $(4, 1)$ is:

If the graph of $y = ax^2 - bx + c$ is as shown below,then the signs of $a$,$b$,and $c$ are:

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$,passing through $(2, 3)$,and the axis is along the $x$-axis.

If the line $7y - 4x = 10$ is a tangent to the parabola $y^2 = 4x$,find the point of contact.

Vedclass Test Series

Exam Paper Generator

Online Exam Module