In the equation 3x2 + 4y2 -18x + 8y +19 = 0, find the center and foci, plot the ends of the axes and of the latera recta, and draw the curve.

Q: Write the standard form of the equation of the circle given x2 - 6x + y2 + 8y + 12 = 36

A: To rewrite the given equation to the standard equation of the circle (x-a)^2+(y-b)^2 =r^2, center…

Q: In the equation 3x2 + 4y2 -18x + 8y +19 = 0, find the center and foci, plot the ends of the axes and…

A: 3x2+4y2-18x+8y+19=0 On simplification, we get…

Q: Write the standard form of the equation of the circle with center (-2, 3) and radius 4.

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Q: Find the standard form of the equation of the circle with a diameter having two points (1, -6) & (7,…

A: The end points of diameter of the circle are (1,-6)  and (7,2). The standard form of equation of…

Q: Derive the standard equation of a circle if its general equation is x² + y² - 10x - 6y + 14 = 0.…

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Q: Y² – 16X² + 64X – 208 = 0

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Q: 1. x²-2x-24y+1=0 Standard Form Equation: a. Vertex: b. Focus: C. Length of LR: d. Directrix:

A: Topic = Parabola As per guidelines , At a time only one question with three sub-parts can be…

Q: Find the center and radius of the circle whose equation is x² + 10x + y² – 5y + 4 = 0. The center of…

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Q: determine the radius and the coordinates of the center of the circle which equation x2+y2-4x+8y+3=0

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Q: If P=(-2,-1) and Q=(-6,-3) are the endpoints of the diameter of a circle, find the equation of the…

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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.