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: Question 3 Sketch the circle for the following equation. (x+3)^(2)+(y-3)^(2)=4. Clear All Draw:…

A: Given data ÷ x+32+y-32=4 We need to sketch the graph÷ Important points from the equation…

Q: What is the equation of a circle having (10,2) and (6,-4) as endpoints of its diameter? x² + y² 16x…

A:

Q: II - Circle 5. Write the equation of the circle with the points (0, 1/2a), (1/2b, 0) as ends of a…

A:

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

A: Equation of an ellipse with foci on y axis and center at origin is given by  x2b2+y2a2=1…

Q: Determine the vertical traces of elliptic and parabolic cylinders in standard form.

A: Firstly the trace of a surface which is actually a cross section or the curves of intersection of a…

Q: What is the family of curves for all parabolas with axes parallel to the y-axis.

A:

Q: Consider the equation of the circle given as: 3x^2 + 3y^2 + 6x - 4y=0.The corresponding center of…

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

Q: Find the center-radius form of the equation of the circle. 21) center (-/3, -7), radius 3 A) (x -…

A: Here we will find the equation of circle in centre-radius form,

Q: Determine the equation for the parabola with the given characteristics: focus at (2,6); directrix at…

A: Parabola

Q: Find the focus of middle point chords of the parabola y² = tax, of whic Subtend a of the parabola.…

A:

Q: how to determine the maximum and minimum distance of an ellipse given the major axis=477,736 and…

A: Length of the major axis is 477,736 Length of the minor axis is 477,078 We need to calculate the…

Q: 4. Find the equation of the ellipse assuming the form + = 1 if distance between foci 4, between…

A: Use simple standard equation

Q: What is the equation of the circle in standard form whose endpoints of a diameter are at A(4, – 5)…

A: Given query is to find the equation of the circle.

Q: Find the equation of a circle that has a diameter with endpoints (5, 2) and (1, -6). A (x- 3)2 - (v…

A:

Q: Write equations in tbe given form for an ellipse centered at (3,4) with vertical axis of length 10…

A: The general equation of ellipse in rectangular form is :  x-h2a2+y-k2b2=1 . Note the below result…

Q: uestion 1: For the graph of the circle below whose equation is of the form (x-h)²+(y-k)² = r2, enter…

A:

Q: 23) Foci: (-5, 13), (-5, 7) Endpoints of major axis: (-5, 15), (-5,5)

A:

Q: Find the center-radius form of the equation for the circle with a diameter of endpoints (-1, 3) and…

A:

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.