Reduce the equation to a standard form and describe the curve completely by providing the important aspects of the curve, if: ● CIRCLE - center and radius ● PARABOLA - direction of the opening, vertex, focus, ends of latus rectum, and directrix ● ELLIPSE - center and direction of major axis, vertices/co-vertices (endpoints of the major and minor axes), foci, ends of latera recta, and directrices ● HYPERBOLA - center and direction of transverse axis, vertices/endpoints of the transverse and conjugate axes, foci, ends of latera recta, directrices, and asymptotes. given: 2y^2 + x + 8y - 4 = 0

Q: Give the standard equation of the parabola with focus (-3,0) and directrix x=3

A: Standard equation of parabola is y2=±4ax Given that focus of parabola is (-3,0) and directrix is…

Q: Find the equation of the parabola and the length of the latus rectum with directrix y = -2 and focus…

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Q: Find the standard form of the equation of th parabola with: and Focus (-2, 6) Directrix X = 8

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Q: What is the equation for the parabola below in terms of its focus and directrix? y = _____

A: Given: equation of the parabola

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Q: Determine an equation for the parabola with focus (3,2) and directrix y = -4.

A: Since, directrix is vertical use equation of parabola that opens up or down.     (x-h)2 = 4p(y-k)…

Q: Find the equation of the parabola with focus (-3, 0) and directrix x-3.

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Q: Find an equation for the curve traced by the point P(x, y) if the distance from P to the vertex of…

A: First find the vertex and focus of x^2=4y

Q: Reduce each equation to a standard form and describe the curve completely. If the curve is a:…

A: The standard form of the circle is: (x-h)2+(y-k)2=r2 where (h,k) is the center and r is the radius…

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 2) and directrix…

A: Given:            Focus of parabola is : F(0,2)Directrix is:​y=−2.

Q: identify the surface defined by the equation and match it to the appropriate graph

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Q: Find the equation of the parabola with directrix x+1=0 , axis y=1 and the length of the latus rectum…

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Q: Find an equation for the parabola with focus (0, -4) and directrix y =

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Q: Find the Parabola with Focus (7,-2) and Directrix x=-9

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Q: 2. Determine the orthogonal trajectory of the family of hyperbolas y? – 121x? = c. Sketch some of…

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Q: Determine the equation of the parabola using the given information. Focus (0, −3) and directix y =…

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Q: Graph the parabola with a focus of ( – 2, 1), a directrix of y = 7, and goes through the point (4,…

A: We have to find the equation of parabola.

Q: Find an equation of the parabola in standard form: with focus at F(7,-1) and directrix 6 units from…

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Q: 9. Identify the center and radius of a circle with equation (x-7) +(y+6) = 16. Ocenter at (7,-6);…

A: Given problems:-

Q: A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius of…

A: The correct option is B . See the explanation in the attachment below...

Q: Determine the standard form of an equation of the parabola with focus (1, 2) and directrix x = 7.

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Q: Find a Cartesian equation for the curve and identify it as either a hyperbola, circle, limaAson,…

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Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: Here we find the equation of parabola.

Q: Find the standard form of the equation of a parabola with focus (8,0) and directrix x = -8.

A: Focus is, a, 0=8, 0⇒a=8 Directrix is x=-8.

Q: Use the Distance Formula to show that the equation of the parabola with focus F(0, 1) and directrix…

A: Given that Focus of the parabola is F0, 1 and Directrix is y=-1 We have to prove that y=14x2 is the…

Q: Reduce each equation to a standard form and describe the curve completely by providing the important…

A: 1  x2+y2+6x+8y=-9

Q: Reduce each equation to a standard form and describe the curve completely by providing the important…

A: Step:-1 Given that 3x2−2y2−12x+12y=12 It can be written as…

Q: Find the general form and graph of the focal width of a parabola is 14 units and its vertex can be…

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Q: Find a Cartesian equation for the curve and identify it as an ellipse, circle, limAson, parabola, or…

A: Cartesian equation for the curve is r = 3 cos(θ) Now x = r cos(θ)   ……(1)

Q: Find the focus and directrix of the parabola y = -x2, and sketch the graph.

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Q: 1. Marsha was completing the steps for a parabola that has a focus at (5,-2) with directrix at y =…

A: Formula:-1)Distance between two points (x1,y1) & x2,y2 is d=(x1-x2)2+(y1-y2)22)Distance of a…

Q: Find an equation of the parabola with focus (4, 4) and directrix x=0.

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Q: Find the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4

A: Given: Equation of directrix:y=3……1Equation of axis:x=0……2Length of latus rectum:4……3

Q: An ellipse is a circle if and only if a-b equals what?

A: Given that an ellipse is a circle.

Q: Two parabolas are given: - C₁ is the curve of intersection between y = 1-2² and 2 = - C₂ is the…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find the standard form of the equation of the parabola with the given characteristics. Focus: (1,…

A: Given: A rough sketch of the parabola shall be as follows:

Q: Find the equation of a parabola whose focus is at(2,-3) and directrix's equation is x=5.

A: Distance between the point x1 , y1 and a lineax+by+C=0 is ax1+by1+Ca2+b2

Q: Determine whether the curve 12x² + 3y² = 36 is a circle, parabola, ellipse, or hyperbola.

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Q: Find the equation of a parabola that has focus at (-4,0) and directrix 2

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Q: Find the focus, directrix, and focal diameter of the parabola y = x², and sketch its graph.

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Q: Find the focus diretrix, and focal diameter of the parabola: x^2=-8y

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Q: Determine the standard form of the parabolic equation x = 1/2 (y + 5)2 − 2. Further, characterize…

A: x=12y+52-2 On simplification, we get ⇒12y+52=x+2⇒y+52=2x+2⇒y--52=2x--2 Now it is in the form of…

Q: Give equations for the following curves: • Parabola with vertex at the origin - 1 • Parabola with…

A: I have Provided this answer in step-2.

Q: Sketch the following: A. Straight line with slope and y-intercept equal. B. Circles with center on…

A: Topic:- geometry  Note:- as per our guideline if more than three subparts posted than only first…

Q: Determine the equation and sketch the graph the parabola given focus at (12, 3) and directrix at x =…

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Q: Given an ellipse x2/a2 +y2/b2= 1, a  b, find the  equation of the set of all points from which there…

A: (Note: We are entitled to solve only one question at a time) Given: x2a2+y2b2=1, where a≠b. To Find:…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.