Find Vertex of Parabola Calculator

Parabola is one of the conic sections whose eccentricity is equal to  1. Eccentricity of an conic section is defined as the how it is deviating from circular  shape .The parabola has three major components.this article will help you to find vertex of parabola as a calculator.
i)Vertex
ii)Focus
iii) Directrix
iv)Axis

Expalnation to find vertex of parabola calculator

Definition of parabola :

Parabola is the locus of points whose distance from fixed line, called as  directrix, and a from a fixed point , called as focus,is equal.

Vertex of parabola :-

The vertex of parabola is the point where the parabola changes its direction.It is apoint where the parabola crosses its axis.

Features of vertex of a parabola :-

i)It lies on the parabola

ii)It  lies on axis of parabola.

iii)It is apoint equidistant from focus and directrix of parabola.

Standard forms of a parabola :-

parabolas having vertex at (0,0)

i)Y² = 4aX

ii)Y² = -4aX

iii)X² = 4aY

iv)X² = -4aY

Parabolas having vertex at (h,k)

i)(Y-k)2 = 4a(X-h)

ii)(Y-k)2 = -4a(X-h)

iii)(X-k)2 = -4a(Y-h)

iv)(X-k)2 = 4a(Y-h)

Calculation of vertex of parabola :-

i) parabola is to be transformed into one of the standard forms given above  to find the  vertex of parabola.

examples to find vertex of parabola calculator

Ex:1
Given the equation of parabola Y² = 16X find the focus of parabola
solution:
Comparing with standard form of equation
Y² = 4aX
we get vertex of parabola as
(0,0)

EX 2:FInd vertex of parabola
Y² + 2y +1 = 3x-9
solution:-
transforming into standard equation
=> (y+1)² =3(x-3)
on comparing with (Y-k)² =4a(X-h)
vertex (h,k)=(3,-1)

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Ex 3: Find vetex of parabola
X²-2x+4 = 2Y-1
solution:
Converting to standard form (X-h)² =4a(Y-k)
X²-2x+4 = 2Y+1
=> (X-2)² = 2(Y+1/2)
=> (h,k)=  (2 , -1/2).