If a parabola has the focus at ( 0 , − 1 ) \left(0,-1\right) and a directrix line y = 1 y=1 y = 1 , find the standard equation for the parabola.

Hey, everyone. Let's give this problem a try. So we're told if a parabola has the focus point 0 negative 1, and the directrix line y equals 1, find the standard equation for the parabola. Okay. So to solve this problem, what you need to do is remember what the standard form for any parabola is, and that is we have 4p times y minus k is equal to x minus h squared. And what we want to do is piece this equation together so there's only a y and a k remaining The or excuse me, only a y and an x remaining because those are the only variables that we really have at the end. Now what I can do is work backwards given the focus and the directrix. And if I think about what this means as far as a graph goes and by the way, we don't actually need to graph this. That's on the instructions. I'm just, doing this so we can have this for reference. What we can do is recognize that the focus point is at 0 negative one, which is right down there. And the directrix line is at y equals one which would be somewhere up here. Now if the focus point and directrix line are both this distance apart, the parabola's vertex is going to be somewhere in between these or somewhere in the center because the parabola's vertex is between the directrix and focus. So this would be the parabolas center which would be at 0. So we're at the origin in this problem. Now what we need to do from here is find out what the p value is. And we can find the p value by recognizing that it takes 1 unit to get to the directrix line, and 1 unit to get down to the focus point. So p is going to be 1, but since we see that the focus point is down it's going to be negative one because the directrix line is gonna be opposite the direction it opens. So this is going to curve down, meaning we would have a negative p value, and because of this, this allows us to assemble our equation because we have the vertex and we have the p value, so I recognize that p is negative one, and the h and the k are both going to be 0. So that means our equation is going to be 4 times negative one, times y is equal to x squared, and 4 times negative one is negative 4. So we'll have negative 4 y equals x squared, and that is going to be the equation for our parabola. So hope you found this helpful, thanks for watching.

If a parabola has the focus at (0,−1)\left(0,-1\right) and a directrix line y=1y=1y=1, find the standard equation for the parabola.

4(y−1)=x24\left(y-1\right)=$$x^24(y$$−1)=x2

−4(y+1)=x2-4\left(y+1\right)=$$x^2$$−4(y+1)=x2

Skip topic navigation

0. Review4h 36m

Algebraic Expressions
37m

Exponents
32m

Polynomials Intro
19m

Multiplying Polynomials
36m

Factoring Polynomials
1h 2m

Radical Expressions
15m

Simplifying Radical Expressions
35m

Rationalize Denominator
15m

Rational Exponents
4m

Pythagorean Theorem & Basics of Triangles
17m

1. Equations & Inequalities3h 26m

Linear Equations
31m

Rational Equations
21m

The Imaginary Unit
6m

Powers of i
11m

Complex Numbers
41m

Intro to Quadratic Equations
18m

The Square Root Property
11m

Completing the Square
12m

The Quadratic Formula
19m

Choosing a Method to Solve Quadratics
9m

Linear Inequalities
22m

2. Graphs & Functions4h 0m

Graphs and Coordinates
7m

Two-Variable Equations
23m

Lines
1h 12m

Intro To Functions And Graphs
35m

Common Functions
5m

Transformations
45m

Function Operations
21m

Function Composition
29m

3. Polynomial and Rational Functions3h 18m

Quadratic Functions
49m

Understanding Polynomial Functions
34m

Graphing Polynomial Functions
30m

Intro to Rational Functions
9m

Asymptotes
35m

Graphing Rational Functions
38m

4. Inverse, Exponential, and Logarithmic Functions2h 28m

Intro to Exponential Functions
9m

Graphing Exponential Functions
25m

The Number e
8m

Intro to Logarithms
22m

Graphing Logarithmic Functions
18m

Properties of Logarithms
27m

Solving Exponential & Logarithmic Equations
35m

5. Trigonometric Functions5h 25m

Angles in Standard Position
12m

Coterminal Angles
8m

Complementary & Supplementary Angles
10m

Converting between Degrees & Radians
8m

Trigonometric Functions on Right Triangles
45m

Special Right Triangles
30m

Cofunctions of Complementary Angles
26m

Solving Right Triangles
23m

Defining the Unit Circle
14m

Trig Functions on the Unit Circle
9m

Common Values of Sine, Cosine, & Tangent
11m

Reference Angles
38m

Reciprocal Trig Functions on the Unit Circle
6m

Graphs of the Sine and Cosine Functions
32m

Phase Shifts
14m

Graphs of Secant and Cosecant Functions
10m

Graphs of Tangent and Cotangent Functions
21m

6. Analytic Trigonometry4h 15m

Inverse Sine, Cosine, & Tangent
28m

Evaluate Composite Trig Functions
44m

Linear Trigonometric Equations
28m

Introduction to Trig Identities
1h 4m

Sum and Difference Identities
1h 3m

Double Angle Identities
16m

Solving Trig Equations Using Identities
9m

7. Applications of Trigonometry1h 38m

The Law of Sines
49m

The Law of Cosines
30m

Area of SAS & ASA Triangles
19m

8. Polar Coordinates and Complex Numbers4h 20m

Polar Coordinate System
29m

Convert Points Between Polar & Rectangular Coordinates
26m

Convert Equations Between Polar & Rectangular Forms
29m

Graphing Other Common Polar Equations
39m

Graphing Parametric Equations
12m

Eliminate the Parameter
32m

Writing Parametric Equations
21m

Graphing Complex Numbers
6m

Polar Form of Complex Numbers
22m

Products and Quotients of Complex Numbers
14m

Powers of Complex Numbers (DeMoivre's Theorem)
23m

9. Vectors2h 25m

Geometric Vectors
28m

Vectors in Component Form
32m

Direction of a Vector
23m

Unit Vectors and i & j Notation
27m

Dot Product
22m

Cross Product
11m

10. Systems of Equations & Matrices4h 5m

Two Variable Systems of Linear Equations
1h 7m

Introduction to Matrices
1h 11m

Determinants and Cramer's Rule
1h 3m

Graphing Systems of Inequalities
42m

11. Analytic Geometry2h 36m

Introduction to Conic Sections
6m

Circles
26m

Ellipses: Standard Form
33m

Parabolas
36m

Hyperbolas at the Origin
40m

Hyperbolas NOT at the Origin
12m

12. Sequences, Series, and Induction1h 22m

Sequences
40m

Arithmetic Sequences
25m

Geometric Sequences
15m

13. Combinatorics and Probability1h 45m

Factorials
11m

Combinatorics
46m

Probability
47m

11. Analytic Geometry

Parabolas

Algebra & Trigonometry

11. Analytic Geometry

Parabolas

이전 문제다음 문제

Algebra & Trigonometry 때문에 힘들어하고 계신가요?

저희를 신뢰하는 수천 명의 학생들이 시험 합류하세요!

객관식

If a parabola has the focus at $open paren 0 comma negative 1 close paren$ and a directrix line $y=1$ , find the standard equation for the parabola.

$4y=x^2$

$4$\left$(y-1$\right$)=x^2$

$-4y=x^2$

$-4$\left$(y+1$\right$)=x^2$

0 댓글

이전 문제다음 문제

5:28m

다음 시청

마스터 Horizontal Parabolas가 Callie Rethman 짧은 영상으로 설명해 줍니다

Algebra & Trigonometry 때문에 힘들어하고 계신가요?

If a parabola has the focus at (0,−1)\(\left\)(0,-1\(\right\)) and a directrix line y=1y=1y=1, find the standard equation for the parabola.

다음 시청

If a parabola has the focus at $open paren 0 comma negative 1 close paren$ and a directrix line $y=1$ , find the standard equation for the parabola.