Ellip - Study guides, Class notes & Summaries

Equation of a Circle (x-h)^2 + (y-k)^2 = r^2 distance formula d = square root of (x-h)2 + (y-k)^2 - used to find the radius a.k.a. the distance from the center of a circle from a point on the circle. Center of a Circle (h,k) The center of a circle is equidistant from every point on the circle Standard Equation of a Parabola symmetrical over y axis (x-h)^2=4p(y-k) symmetrical over x axis (y-k)^2=4p(x-h) Directrix & Focus every point on a parbola is the same d...

by looking at the vertices and co-vertices how do you know if it is vertical or horizontal? -if the vertices are on the x-axis, it is horizontal, if the vertices are on the y-axis, it is vertical -remember horizontal goes with "x" and vertical gets with "y" -your vertices always go on your major axis and the co-vertices on the minor axis how do u write the equation of an ellipse? x2/a2 + y2/b2 00:02 01:28 what should you look out for if she's talking about the he...

Circle Collection of points equidistant from the center. Equations for Circle (x-h)^2 + (y-k)^2 = r^2 Where (h,k) = center And r = radius 00:24 01:28 Distance Formula The square root of (x2-x1)^2 + (y2-y1)^2 Parabola Set of points equidistant from a focus and the directrix. Equations for Parabolas (x-h)^2 = 4p(y-k) Up if p>0, down if p<0 (y-k)^2 = 4p(x-h) Right if p>0, left if p<0 p = distance (h,k) = vertex Directrix E...

Axis of symmetry The line that a parabola is symmetrical about. The vertex and focus are on the axis of symmetry What is the equation of a circle with center at (3, -2) and radius = 8? (x - 3)² + (y + 2)² = 64 00:01 01:28 What is the equation of a circle with center at (-7, -1) and radius = 3? (x + 7)² + (y + 1)² = 9 What is the equation of a circle with center at (1, 5) and radius = 2? (x - 1)² + (y - 5)² = 4 What is the equation of a circle with ...

equation for asymptotes y-y1 = m (x-x1) When are ellipsis's vertical? when biggest denominator is under Y term 00:03 01:28 When are ellipsis's horizontal? when biggest denominator is under X term How can you identify the "a" term for Ellipsis's? it is always under the first term When are hyperbola's vertical? when Y term comes first in sequence when are hyperbola's horizontal? when X term comes first in sequence Where do you begin ...

Circle A defined as a set of points that are equidistant (the same distance) from a certain point Hyperbola the set of points in a plane whose distances to two fixed points in the plane have a constant difference; a curve consisting of two distinct and similar branches, formed by the intersection of a plane with a right circular cone when the plane makes a greater angle with the base than does the generator of the cone. 00:01 01:28 Ellipse a plane curve such that the s...

equation for parabola going through horizontal twice x²=4py equation for parabola going through vertical twice y²=4px 00:01 01:28 directrix of x²=4py y=-p directrix of y²=4px x=-p what is the symbol for focus? p the coordinates for the foci in x²=4py? (vertex,vertex±c) the coordinates for the foci in y²=4px? (vertex±c,vertex) what is p? the distance from the vertex to the focus what is the equation for a circle (x...

Introduction and main results. This paper is a contribution to the study of “explosive behavior” in certain systems of elliptic and parabolic PDEs. Our investigation is motivated by a question regarding the dynamics of a viscous, heat-conducting fluid. In general, the flow of such a fluid is governed by a system of balance equations for momentum, mass, and energy. Under the assumptions of the so-called Boussinesq approximation, this system reduces to the Navier–Stokes equations for a...

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"Dive into ellipses with this detailed guide, beginning with a summary of key concepts before progressing through three levels of questions. Level 1 focuses on foundational understanding, Level 2 explores practical applications, and Level 3 offers challenging problems. With clear explanations and illustrative diagrams, this resource is ideal for learners seeking to deepen their grasp of ellipses."