Hyperbola Equation Calculator given foci and vertices

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).