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Hace 3 días · The standard form equation of a hyperbola with a vertical transverse axis is \[\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1.\] The vertices are located at \((h,k-a)\) and \((h,k+a)\).
2 de jul. de 2024 · Which is the standard form of the equation of a parabola with a focus of (0, -3) and its vertex at the origin?
23 de jun. de 2024 · General Equations of Degree Two. A general equation of degree two can be written in the form \[ Ax^2+Bxy+Cy^2+Dx+Ey+F=0. \nonumber \] The graph of an equation of this form is a conic section. If \(B≠0\) then the coordinate axes are rotated. To identify the conic section, we use the discriminant of the conic section \(4AC−B^2.\)
29 de jun. de 2024 · vertex form. A quadratic function in the form y=a (x-h)^2+k, where (h,k) is the vertex of the parabola and x=h is its axis of symmetry. intercept form. the form y=a (x-p) (x-q), where the x-intercepts of the graph are p and q. monomial.
Hace 6 días · Show that the following system of parametric equations describes a line or a parabola: $$\begin{cases} x=a_1t^2+b_1t+c_1 \\ y=a_2t^2+b_2t+c_2 \end{cases}, t\in\mathbb{R}.$$
11 de jun. de 2024 · The following are the observations made from the standard form of equations of a parabola: A parabola is symmetrical w.r.t its axis. For example, y 2 = 4ax is symmetric w.r.t the x-axis, whereas x 2 = 4ay is symmetric with respect to the y-axis.
2 de jul. de 2024 · Which of the following is the equation of a hyperbola with center at (0, 0), with a = 4, b = 1, opening horizontally? x^2/1-y^2/16=1 y^2/16-x^2/1=1 x^2/16-y^2/2=1 x^2/16-y^2/2=1 Identify this conic section. xy = 25 line circle ellipse parabola hyperbola
