A latus rectum for an ellipse is a line segment perpendicular to the major axis at a focus, with endpoints on the ellipse, as shown in the figure below. y b Latus rectum -b Foci Show that the length of a latus rectum is 2b²/a for the ellipse + = 1 with a > b. b2 The foci of the given ellipse are (+cv ,0), where c2 = a2 - b2. If the endpoints of one latus rectum are the points (c, tk), then the length of one latus rectum is Substitute one of the endpoints into the given equation for the ellipse and solve for k. = 1 1 1- a2 k2 = a2 k2 = Substitute b2 for a² - 2. a? k = Thus, the length of a latus rectum for the given ellipse is 2k =

Q: A line segment of length a + b runs from the x-axis to the y-axis. The point P on the segment lies a…

A: Given A line segment of length a + b runs from the x-axis to the y-axis. The point P on the segment…

Q: 10. Find an equation for the ellipse with the length of the minor access of 10, the focus on the y-…

A:

Q: Find the end points of the minor and major axis for the graph of the ellipse (x – 4)? 25 (y – 6)² 1…

A:

Q: What is the eccentricity of an ellipse 9x2+y2+18x-12y-180=0

A:

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

A: The standard equation of ellipse when a>b is given as  x2a2+y2b2=1......(1)

Q: Determine the standard equation of the ellipse using the stated information.   Center at ​(5​,3​);…

A:

Q: satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by…

A: We will solve the following.

Q: A line segment with endpoints on an ellipse and passing through a focus of the ellipse is called a…

A:

Q: The ellipse (x²/16) + (y²/9) = 1 is shifted k units to generate the ellipse a. Find the foci,…

A: Given: x216+y29=1⇒ a2=16   and  b2=9⇒a=4   and…

Q: The arch of a tunnel is in the form of a semi-ellipse. The distance between the bases of the arch is…

A: From the given information the current situation can be represents as shown below, From the above…

Q: then find the end points of the minor and major axis for the graph of this ellipse. Maximum point on…

A: Compare the given equation of the ellipse with standard form of ellipse with center at origin,…

Q: Find the standard form of the equation of the ellipse with the given characteristics. Foci: (0, 0),…

A: The standard equation of ellipse is x-h2a2+y-k2b2=1.................(1)

Q: Find the center, vertices, foci, and eccentricity of the ellipse. 9x2 + 4y2 − 36x + 40y − 8 = 0

A:

Q: The Earth revolves around the Sun along an ellipse. The Sun lies in the focus of the ellipse. The…

A:

Q: An arched footbridge over a 100 foot river is shaped like half of an ellipse. The maximum height of…

A: Given that:                    Width of river, 2a = 100 ftMaximum height of bridge, b=20 ft   NOTE:…

Q: An ellipse has its foci at (−1, 0) and (7, 0), and eccentricity 0.4. Find the (lengths of the)…

A:

Q: A window is constructed with the top half of an ellipse on top of a square. The square portion of…

A:

Q: The ellipse with semi-major axis a, eccentricity e and foci F1 and F2 intersects the circle with…

A: The principle of ellipse is what we have to use here. a is the semi major axis of an ellipse.  Then…

Q: draw the ellipse when the distance of its focus from its directrix is equal to 60mm and eccentricity…

A:

Q: 3) A large racetrack can be modeled by the ellipse x2 + = 1, where x and y are measured in…

A: An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the…

Q: 4. Consider the ellipse which has its center at (-1, 5), a vertex at (-1, 0), and a covertex at (-5,…

A:

Q: The ellipse (x2/9) + (y2/25) = 1 is shifted 3 units to the left and 2 units down to generate the…

A: Given that on shifting the ellipse x29+y225=1 by 3 units to the left and 2 units to down then new…

Q: Center at (2 , −1), fixed sum is 8, focus at (2, 0) Find the standard equation of the ellipse that…

A: I have stated the used formula in the solution.

Q: An arched footbridge over a 100 foot river is shaped like half of an ellipse. The maximum height of…

A: Since the bridge is elliptical which is arched over 100 ft of river and the maximum height of the…

Q: Find an equation for the ellipse that satisfies the given conditions. Length of mimor axis: 10, foci…

A:

Q: 10. A rectangle with sides parallel to the coordinate axes is inscribed in the ellipse +4 = 1. Find…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the largest triangle that can be inscribed in the ellipse (x2/a2)+(y2/b2)=1 (assume the…

A:

Q: Find an equation of the ellipse drawn below, then find its foci. YA Select one: 1 a. (x²/4)-(y²2/9)…

A:

Q: Which is NOT true about ellipse? O the length of the minor axis is always longer than the major…

A: We need to find which is not true about ellipse In ellipse we have two axis minor axis and major…

Q: Consider the parabola P with equation x^2 = 20 (y - k) and whose directrix has equation y = −7. The…

A: This question is related to conic section , we will use the give conditions to find the equation of…

Q: Charles and Bernice ("Ray") Eames were American designers who made major contributions to modern…

A: Draw the Ellipse and write major axis and minor axis then use formula to find out the foci.

Q: 12 Consider the graph of the ellipse. which is drawn to scale. This ellipse has an eccentricity of…

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

Q: The earth revolves around the sun along an ellipse. The sun lies in the focus of the ellipse. The…

A: Given: The earth revolves around the sun along an ellipse. The sun lies in the focus of the ellipse.…

Q: help with a, b and c please

A: We have to find the points on the ellipse that are farthest from point (1,0).

Q: Find the standard form of the equation of the ellipse with the given characteristics.  Foci:…

A: Please rate

Q: The arch of the bridge below is half an ellipse, a "semi-ellipse". As shown in the figure below, the…

A: Given- A arch which is in shape of semi ellipse and having it's length and height as 148m and 58m…

Q: 3. What are the lengths of the major and minor axes of this ellipse = 1? Major Axis: 6 units, Minor…

A:

Q: the earth revolves around the sun along an ellipse. the sun lies in the focus of the ellipse. The…

A: The earth revolves around the sun along an ellipse. The sun lies in the focus of the ellipse. The…

Q: The Earth revolves around the Sun along an ellipse. The Sun lies focus of the ellipse. The largest…

A:

Q: e of the 4 points of intersection, as shown in the diagram. Let x be the length of P F1 and y the…

A: Ellipse

Q: 1. Find the standard equation of the ellipse which satisfies the given conditions. 1. foci (-7; 6)…

A: We have to find standard equation of the ellipse which satisfy the given conditions- 1. Having foci…

Q: 4. The Earth revolves around the Sun along an ellipse. The Sun lies in the focus of the ellipse. The…

A: Given that, the largest distance from the Sun to the Earth is 152.1 million kilometres, and the…

Q: A line segment with endpoints on an ellipse, perpendicular to the major axis, and passing through a…

A:

Q: An ellipse is drawn using the gardener’s method as follows. Two pins are stuck on a corkboard…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 7. The foci of an ellipse are located at (0, 6) and (0, -6). The sum of the distances from any point…

A: First observe whether it is a horizontal ellipse or vertical ellipse. Then find the center of the…

Q: 10. The arch of a bridge is in the shape of a semi-ellipse having a horizontal span of 90m and a…

A: Let's find height.

Q: Consider the ellipse with the given characteristics and center at the origin. foci: (+3, 0); major…

A:

Q: 3. The ellipse defined by the equation 2x² + y² + 4x – 9y = 7. Major axis parallel to: Graph: 10…

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.