## Hyperbola Equation Calculator

## Hyperbola Equation:

## FAQs

**How to find the equation of a hyperbola given the vertices and foci?** The equation of a hyperbola with vertices and foci can be found using the distance formula and the properties of the hyperbola’s foci and vertices.

**How do you find the equation of a hyperbola with vertices and asymptotes?** To find the equation of a hyperbola with vertices and asymptotes, you can determine the center, use the asymptote equations, and apply the standard hyperbola equation formula.

**How do you find the equation of a parabola with vertices and foci?** For a parabola, the equation is usually given as `(x-h)^2 = 4p(y-k)`

where (h, k) is the vertex and `p`

is the distance from the vertex to the focus.

**How do you write an equation with vertices and foci?** For a hyperbola, the equation is usually written as `(x-h)^2/a^2 - (y-k)^2/b^2 = 1`

or `(y-k)^2/a^2 - (x-h)^2/b^2 = 1`

where (h, k) is the center, `a`

is the distance from the center to a vertex, and `c`

is the distance from the center to a focus.

**How do you find the equation of a hyperbola from points?** To find the equation of a hyperbola from points, you would use the distance formula to determine the distances between the points and the center, then use these values to write the equation in standard form.

**How do you find the equation of a hyperbola given the asymptotes and foci?** Given the asymptotes and foci of a hyperbola, you can determine the center and the distances `a`

and `c`

, then use the standard hyperbola equation formula.

**How to write the equation of a hyperbola given foci and asymptotes?** To write the equation of a hyperbola with given foci and asymptotes, determine the center, distances `a`

and `c`

, and then use the standard hyperbola equation formula.

**How to find the equation of a parabola given the focus and a point?** Given the focus and a point on the parabola, you can find the equation using the focus-directrix property or the vertex-focus property, depending on the orientation of the parabola.

**How do you find the equation of a parabola with a point and focus?** Given a point and the focus of a parabola, you can determine the equation using the distance formula and the properties of the parabola.

**How to find standard form of a parabola with vertex and focus?** The standard form of a parabola can be found using the vertex-focus property, resulting in an equation like `(x-h)^2 = 4p(y-k)`

or `(y-k)^2 = 4p(x-h)`

.

**How do you find the equation of an ellipse given a point and foci?** The equation of an ellipse given a point and foci can be determined using the properties of the ellipse and the distance formula.

**What is the formula for a hyperbola?** The general formula for a hyperbola is `(x-h)^2/a^2 - (y-k)^2/b^2 = 1`

or `(y-k)^2/a^2 - (x-h)^2/b^2 = 1`

where (h, k) is the center, `a`

is the distance from the center to a vertex, and `c`

is the distance from the center to a focus.

**What is the equation of a hyperbola given the vertices?** The equation of a hyperbola given the vertices can be written using the distance formula and the properties of the hyperbola’s foci and vertices.

**How do you find the equation of a function with points?** To find the equation of a function given points, you would typically use methods like linear regression, polynomial interpolation, or fitting the data to a suitable function type.

**How do you find the equation of a parabola from a graph?** To find the equation of a parabola from a graph, you can use the vertex form of the parabola equation, which is `y = a(x-h)^2 + k`

, where (h, k) is the vertex.

**What is the equation of the hyperbola that has foci?** The equation of a hyperbola with foci can be written using the standard form equations mentioned earlier, `(x-h)^2/a^2 - (y-k)^2/b^2 = 1`

or `(y-k)^2/a^2 - (x-h)^2/b^2 = 1`

.

**How to find the equation of a hyperbola given foci and transverse axis?** Given the foci and the length of the transverse axis, you can determine the equation of the hyperbola using the standard form equations and properties.

**What is the equation of a hyperbola with foci and constant difference?** The equation of a hyperbola with foci and a constant difference can be derived using the properties of the hyperbola and the relationship between the distances.

**How do you find the equation of a parabola given two points?** To find the equation of a parabola given two points, you can use the vertex-focus or the focus-directrix property, depending on the information provided.

**How to find the equation of a parabola given the vertex, focus, and Directrix?** With the vertex, focus, and directrix information, you can determine the equation of a parabola using the properties of parabolas and their focus-directrix relationship.

**What is the equation of a parabola with vertex at the origin and the given focus at (5, 0)?** For a parabola with the vertex at the origin and the focus at (5, 0), the equation is of the form `x^2 = 4py`

.

**What are the 3 parabola equations?** The three common forms of parabola equations are `y = ax^2 + bx + c`

(quadratic form), `x = ay^2 + by + c`

(quadratic form), and `y = a(x-h)^2 + k`

(vertex form).

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