Find equation of parabola given focus and directrix calculator

Q: How do you find standard form when given focus and Directrix?

The standard form is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)2 = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.

Home
»
Geometry
»

Table of Contents Show

Number Line
Number Line
How to Use the Parabola Calculator?
What is Meant by Parabola?
How do you find the equation of a parabola when given focus?
How do you find standard form when given focus and Directrix?
What is parabola using focus and Directrix?

Parabola Equation Solver Calculator

Vertex :

Focus :

Standard Equation:

Equation in Vertex Form:

click here for parabola vertex focus calculator.

Parabola Equation Solver based on Vertex and Focus Formula:

   For:
      vertex: (h, k)
      focus: (x1, y1)

• The Parobola Equation in Vertex Form is:
(X-h)2 = 4a(Y-k); ( a = √(h-x1) * (h-x1) + (k - y1) * (k-y1) )

• The Parobola Equation in Standard Form is:
Y = (1/4a)X2 - (h/2a)X + (k + h2/4a); ( a = √(h-x1) * (h-x1) + (k - y1) * (k-y1) )

Related » Graph » Number Line » Similar » Examples »

Our online expert tutors can answer this problem

Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us!

You are being redirected to Course Hero

I want to submit the same problem to Course Hero

Correct Answer :)

Let's Try Again :(

Try to further simplify

Number Line

Graph

Hide Plot »

Sorry, your browser does not support this application

Examples

(y-2)=3(x-5)^2
foci\:3x^2+2x+5y-6=0
vertices\:x=y^2
axis\:(y-3)^2=8(x-5)
directrix\:(x+3)^2=-20(y-1)

parabola-function-calculator

Related » Graph » Number Line » Similar » Examples »

Our online expert tutors can answer this problem

Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us!

You are being redirected to Course Hero

I want to submit the same problem to Course Hero

Correct Answer :)

Let's Try Again :(

Try to further simplify

Number Line

Graph

Hide Plot »

Sorry, your browser does not support this application

Examples

directrix\:(y-2)=3(x-5)^2
directrix\:3x^2+2x+5y-6=0
directrix\:x=y^2
directrix\:(y-3)^2=8(x-5)
directrix\:(x+3)^2=-20(y-1)

parabola-function-directrix-calculator

Parabola Calculator is a free online tool that displays the graph for the given parabola equation. BYJU’S online parabola calculator tool makes the calculation faster, and it displays the graph of the parabola in a fraction of seconds.

How to Use the Parabola Calculator?

The procedure to use the parabola calculator is as follows:
Step 1: Enter the parabola equation in the input field
Step 2: Now click the button “Submit” to get the graph
Step 3: Finally, the parabola graph will be displayed in the new window

What is Meant by Parabola?

In Maths, a parabola is one of the types of conic sections. A parabola is a symmetrical plane curve which is formed by the intersection of a right circular cone with a plane surface. It is a U- shaped curve with specific properties. In short, a parabola is a curve such that any point on the curve is at equal distance from a fixed point called locus and a fixed straight line called the directrix. The simplest form of parabola equation is given by y = x2.

How do you find the equation of a parabola when given focus?

Let (x0,y0) be any point on the parabola. Find the distance between (x0,y0) and the focus. Then find the distance between (x0,y0) and directrix. Equate these two distance equations and the simplified equation in x0 and y0 is equation of the parabola.

How do you find standard form when given focus and Directrix?

The standard form is (x - h)² = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)² = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.

What is parabola using focus and Directrix?

What are the focus and directrix of a parabola? Parabolas are commonly known as the graphs of quadratic functions. They can also be viewed as the set of all points whose distance from a certain point (the focus) is equal to their distance from a certain line (the directrix).