1. Fundamental Concepts of Algebra

2. Equations and Inequalities

3. Functions and Graphs

4. Polynomial and Rational Functions

5. Exponential and Logarithmic Functions

6. Systems of Equations and Inequalities

7. Matrices and Determinants

8. Conic Sections

9. Sequences, Induction, and Probability

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In Exercises 37–50, graph each ellipse and give the location of its foci. (x +3)²/9 + (y -2)² = 1<img src="https://lightcat-files.s3.amazonaws.com/problem_images/9a90a3863a2b90cd-1671060005810.jpg" alt="" />

The equation of the red ellipse in the figure shown is x^2/25 + y^2/9 =1Write the equation for each circle shown in the figure. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/f522a6532f1ea822-1676572890043.jpg" alt="" />

Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (-4,0), (4,0); Vertices: (-5,0) (5,0)

In Exercises 1–18, graph each ellipse and locate the foci. x^2/9 +y^2/36= 1

In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Foci: (-2, 0), (2, 0); y-intercepts: -3 and 3

In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Foci: (-5, 0), (5, 0); vertices: (-8, 0), (8,0)

Graph the ellipse and locate the foci. (x^2)/36 +(y^2)/25 = 1

Solve Applied Problems Involving Ellipses

The Ellipse

Whispering Gallery and Ellipse

In Exercises 37–50, graph each ellipse and give the location of its foci. (x − 2)²/9 + (y -1)² /4= 1<img src="https://lightcat-files.s3.amazonaws.com/problem_images/df04027a806fed6c-1671023008944.jpg" alt="" />

In Exercises 1–18, graph each ellipse and locate the foci. x^2/(9/4) +y^2/(25/4) = 1

Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis horizontal with length 12; length of minor axis = 4; center: (-3,5)

In Exercises 1–18, graph each ellipse and locate the foci. x^2/16 +y^2/4 = 1

Conic Sections: Find Equation of an Ellipse Given Major / Minor Axis Length

In Exercises 37–50, graph each ellipse and give the location of its foci. 9(x − 1)²+4(y+3)² = 36

In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Major axis horizontal with length 8; length of minor axis = 4; center: (0, 0)

Conic Sections: Graphing Ellipses  Part 1

Conic Sections: Graphing Ellipses Part 2

In Exercises 19–24, find the standard form of the equation of each ellipse and give the location of its foci. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/667b9c4051c9c47a-1676478446518.jpg" alt="" />

In Exercises 1–18, graph each ellipse and locate the foci. x^2/25 +y^2/64 = 1

In Exercises 49–56, identify each equation without completing the square.

4x^2 - 9y^2 - 8x - 36y - 68 = 0

In Exercises 19–24, find the standard form of the equation of each ellipse and give the location of its foci. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/8eadd88c1e90b744-1676477250854.jpg" alt="" />

Conic Sections, Ellipse, Shifted: Sketch Graph Given Equation

Graphing Conic Sections Part 2: Ellipses

In Exercises 37–50, graph each ellipse and give the location of its foci. (x +3)²+ 4(y -2)² = 16<img src="https://lightcat-files.s3.amazonaws.com/problem_images/431677bd7f28ffcf-1671026095287.jpg" alt="" />

Conic Sections, Ellipse : Graph the Ellipse

Conic: Ellipse Application (Fireplace Arch)

In Exercises 37–50, graph each ellipse and give the location of its foci. (x − 1)²/2 + (y +3)² /5= 1<img src="https://lightcat-files.s3.amazonaws.com/problem_images/9f4a8ef13338dfe7-1671061564746.jpg" alt="" />

In Exercises 1–18, graph each ellipse and locate the foci.4x²+16y² = 64

In Exercises 37–50, graph each ellipse and give the location of its foci. (x − 4)²/9 + (y +2)² /25= 1<img src="https://lightcat-files.s3.amazonaws.com/problem_images/4697211e29547091-1671028231540.jpg" alt="" />

Find the standard form of the equation of an 
ellipse with vertices at (0, -6) and (0, 6), passing through (2, 4).

Graph the ellipse and locate the foci. (y^2)/25 + (x^2)/16 = 1

Ellipse Application

In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Foci: (0, -4), (0, 4); vertices: (0, −7), (0, 7)

In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Major axis vertical with length 10; length of minor axis = 4; center: (-2, 3)

Graph the ellipse and locate the foci. 9x^2 + 4y^2 - 18x + 8y -23 = 0

In Exercises 19–24, find the standard form of the equation of each ellipse and give the location of its foci. <img src="https://lightcat-files.s3.amazonaws.com/problem_images/d7ac7e5ab552ae14-1676477605184.jpg" alt="" />

Ellipses - Application Problems

In Exercises 37–50, graph each ellipse and give the location of its foci. x²/25 + (y -2)² /36= 1<img src="https://lightcat-files.s3.amazonaws.com/problem_images/ca066cbfeb50f4fb-1671058676601.jpg" alt="" />

In Exercises 1–18, graph each ellipse and locate the foci. 25x²+4y² = 100

In Exercises 1–18, graph each ellipse and locate the foci. x² = 1 – 4y²

In Exercises 1–18, graph each ellipse and locate the foci. 7x² = 35-5y²

In Exercises 1–18, graph each ellipse and locate the foci. x^2/49 +y^2/81 = 1

Learn the toughest concepts covered in Algebra with step-by-step video tutorials and practice problems by world-class tutors

College Algebra

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Got Chalk?

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Write Equations of Parabolas in Standard Form

Graph Parabolas With Vertices Not at the Origin

Solve Applied Problems Involving Parabolas

Identify Conics Without Completing the Square

The Parabola

Graph Ellipses Centered at the Origin

Write Equations of Ellipses in Standard Form

Graph Ellipses Not Centered at the Origin

Locate a Hyperbola's Vertices and Foci

Write Equations of Hyperbolas in Standard Form

Graph Hyperbolas Centered at the Origin

Graph Hyperbolas Not Centered at the Origin

Solve Applied Problems Involving Hyperbolas

The Hyperbola

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