Conic Sections

Identifying Conic Sections

Identify the type of the conic section represented by the equation

9 x^{2} - 16 y^{2} = 144

More examples

Identifying Circles

x^{2} + y^{2} - 8 x + 16 y - 1 = 0

is the equation of a circle with center

(h, k)

and radius

r

for:

h =

and

k =

and

r =

More examples

Finding a Circle Using the Center and Another Point

Write the equation of the circle in the form

(x - h)^{2} + (y - k)^{2} = r^{2}

x^{2} + y^{2} + 6 x + 2 y + 3 = 0

. Submit Question

More examples

Finding a Circle by the Diameter End Points

Find the equation of the circle with its diameter end points at A(2, -3) and B(-1, 5).

More examples

Finding the Parabola Equation Using the Vertex and Another Point

Write the equation of the parabola with: Vertex

(- 3, 6)

and

y

-intercept -10

More examples

Finding the Properties of the Parabola

Find the vertex, focus, and directrix of the parabola given by the equation

y^{2} = 4 x

More examples

Finding the Vertex

Find the vertex of the parabola.

h (x) = - x^{2} + 4 x - 4

More examples

Finding the Vertex Form of the Parabola

Find the vertex form of the parabola given by the equation

y = 2 x^{2} - 12 x + 20

More examples

Finding the Vertex Form of an Ellipse

Given the equation of the ellipse

9 x^{2} + 4 y^{2} - 36 x + 8 y - 4 = 0

, find the vertex form.

More examples

Finding the Vertex Form of a Circle

Given the equation of a circle as

x^{2} + y^{2} - 6 x + 8 y + 9 = 0

, find the vertex form of the circle.

More examples

Finding the Vertex Form of a Hyperbola

Given the equation of a hyperbola as

4 x^{2} - 9 y^{2} = 36

, find the vertex form of this hyperbola.

More examples

Finding the Standard Form of a Parabola

Convert the equation to standard form by completing the square on

x

y

. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola.

x^{2} + 12 x - 12 y + 12 = 0

More examples

Finding the Expanded Form of an Ellipse

Find the expanded form of the ellipse with a center at the origin, a horizontal axis length of 10 and a vertical axis length of 6.

More examples

Finding the Expanded Form of a Circle

A circle is defined by the equation

(x - 5)^{2} + (y - 7)^{2} = 81

. Find the expanded form of this circle.

More examples

Finding the Expanded Form of a Hyperbola

Find the expanded form of the hyperbola with center at origin, foci at (0, ±4), and vertices at (0, ±3).

More examples

Identifying Conic Sections

Identifying Circles

Finding a Circle Using the Center and Another Point

Finding a Circle by the Diameter End Points

Finding the Parabola Equation Using the Vertex and Another Point

Finding the Properties of the Parabola

Finding the Vertex

Finding the Vertex Form of the Parabola

Finding the Vertex Form of an Ellipse

Finding the Vertex Form of a Circle

Finding the Vertex Form of a Hyperbola

Finding the Standard Form of a Parabola

Finding the Expanded Form of an Ellipse

Finding the Expanded Form of a Circle

Finding the Expanded Form of a Hyperbola

Popular Problems