Q1 A cross-section of a duct is an ellipse, which has semi-axes a and b, a>b. The duct conveys water. The ellipse area, A, is determined by the formula: A = n ab The perimeter, P, of an ellipse is T/2 P = 4a [ V1-e sin? udu -b² va e = a where e is ellipse's eccentricity. Assume that the duct area A=2 m². Find a and b of the duct for which a minimum of P is attained, provided the duct area A is fixed. Show all your calculations Amin =...... m, bmin- ......m, Pmin=....m

Q: Find the equation, foci, and directrix of the standard ellipse with eccentricity e = 0.6 and focal…

A: The ellipse is a horizontal ellipse as focal vertices lie on the x - axis. Let the standard equation…

Q: The foci of an ellipse: 3x? + 4y? = 12, will be Select one: O (+4,0) O (+1,0) O (0,±1) (+3,0)

A:

Q: Show that if P is a point on an ellipse with foci F1 and F2, directrices d1 and d2 and eccentricity…

A:

Q: 4a² + y = 4

A:

Q: An arch in the form of a semi-ellipse is 50 feet wide at the base and has the height of 16 feet.…

A: Solve for the

Q: find the important parts (vertex, focus, directrix, endpoints of latus rectum and focal point…

A:

Q: Find the equation of the ellipse with foci (±√13, 0) and semimajor axis a = 4. Then find the…

A: Given: The ellipse with foci (±√13, 0) and semimajor axis a = 4.   The standard cartesian form of…

Q: Find an equation for the ellipse with foci F and F' that passes through P. Sketch the ellipse.

A: Given:           Foci of an ellipse: F(0, 6) and  F'(0, -6) and the ellipse passes through point P…

Q: Discuss the relationship between the eccentricity e of an ellipse and the distance z between the…

A: Consider the equation of an ellipse r= Where e is the eccentricity and 0<e<1.

Q: (b) Find the evolute of the ellipse x2 y? =D1

A:

Q: What is the standard form equation of the ellipse that has vertices (0, ±5) and foci (0, ±4)? Select…

A: Vertices(0,5),(0,-5) Foci(0,4),(0,-4) We have to find equation of ellipse

Q: Q1 A cross-section of a duct is an ellipse, which has semi-axes a and b, a>b. The duct conveys…

A: We have the following information. a>b. but a should be less than or equal to b i.e.; a ≤ b. A =…

Q: What is the standard form equation of the ellipse that has vertices (0, ±12) and foci (0, ±2)?

A: We know that the standard equation of the ellipse is (x-h)^2/b^2+(y-k)^2/a^2=1

Q: Find an equation of the ellipse having a major axis of length 12 and foci at (5, 3) and (-3, 3). 2 2…

A: We want to find equation of the ellipse from the given data.

Q: b A LB≈ b≈ 2 Note: Triangle may not be drawn to scale. Given the triangle above, find the following:…

A: Sol

Q: Write the equation of the ellipse 36æ² + 4y? + 72x + 32y – 44 = 0 in standard form (x – h)? p2 (y –…

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.