Reduce each 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. 1)  x^2 + y^2 + 6x + 8y = −9

Q: What is the (unsigned) distance between the vertex and the focus of the parabola given by (x + 4)² =…

A: Given parabola equation,x + 42 = 19y + 5

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Q: Identify the family of curves of an ellipse if the foci are located on the y-axis and centre of the…

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Q: Graph the given parabola and find its focus: Y=X squared

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A: equation of parabola:-

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

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, ±5), length of…

A: Given that hyperbola satisfies the following conditions: Foci=0,±5  and length of transverse axis is…

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…

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A: Given vertex is (0 , 0) and focus on negative y axis focal diameter is 2

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

A: Given:Vertex=0,0Directrix y=-3Equation of parabola:x-h2=4py-k

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

A: First we have to calculate distance from directix to vertex. I.e P Then insert values of center and…

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 the equation for the parabola that has its vertex at the origin and the focal point is 278…

A: Consider the equation of parabola vertex at origin and focus to the right of directrix. y2=4ax…

Q: 6. Find the equation of the ellipse with centre (0,0), one vertex at (0,13) and one focal point at…

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

A: Given: Focus on the negative y-axis, 6 units away from the directrix

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

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Q: Sketch the parabola and line on the same graph. y = x + 4 and y = 2x + 2 %D

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

A: The given equation is 2y2+x+8y-4=0. Rewrite the equation in standard form:…

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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: The equation of the directrix of a parabola is y = 5 and its focus is at (4,-7). What is the length…

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Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (+10, 0), length of…

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Q: Determine the equation of the parabola given the focus at (-10,23/2) and directrix at y=-11/2.

A: Given- Focus -10,232 and directrix y=-112 To Find- The equation of the parabola.

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A: We have the figure as:

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

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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: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

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

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Q: Determine the equation of the parabola given the focus at (-10,23/2) and directrix at y=-11/2.…

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Q: The filament lightbulb is a thin wire that glows when electricity passes through it. The filament of…

A: Given: The given reflector is 7 inches wide and 2 inches deep i.e. (x,y)=(2,3.5)

Q: The parabola has focus (0,-2) and directrix y=2.

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

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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 orthogonal trajectory of family of parabolas represented by the equation…

A: To find orthogonal trajectories of  y2=4ax.

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

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

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Q: Find the vertex focus focal width and equation of the axis for each parabola. y^2+8y+4-6x+0

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

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Q: Suppose a golf ball is driven so that it travels a distance of 200 feet as measured along the ground…

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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.