In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
For the ellipse \(\dfrac{x^2}{36} + \dfrac{y^2}{16} = 1\).
Focus: \(F(\pm \sqrt{20}, 0)\)
Vertices: \(V(\pm 6, 0)\)
Major axis = \(12\)
Minor axis = \(8\)
Eccentricity: \(e = \dfrac{\sqrt{20}}{6}\)
Latus rectum = \(\dfrac{16}{3}\)
In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
For the ellipse \(\dfrac{x^2}{4} + \dfrac{y^2}{25} = 1\).
Focus: \(F(0, \pm \sqrt{21})\)
Vertices: \(V(0, \pm 5)\)
Major axis = \(10\)
Minor axis = \(4\)
Eccentricity: \(e = \dfrac{\sqrt{21}}{5}\)
Latus rectum = \(\dfrac{8}{5}\)
In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
For the ellipse \(\dfrac{x^2}{16} + \dfrac{y^2}{9} = 1\).
Focus: \(F(\pm \sqrt{7}, 0)\)
Vertices: \(V(\pm 4, 0)\)
Major axis = \(8\)
Minor axis = \(6\)
Eccentricity: \(e = \dfrac{\sqrt{7}}{4}\)
Latus rectum = \(\dfrac{9}{2}\)
In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
For the ellipse \(\dfrac{x^2}{25} + \dfrac{y^2}{100} = 1\).
Focus: \(F(0, \pm \sqrt{75})\)
Vertices: \(V(0, \pm 10)\)
Major axis = \(20\)
Minor axis = \(10\)
Eccentricity: \(e = \dfrac{\sqrt{3}}{2}\)
Latus rectum = \(5\)
In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
For the ellipse \(\dfrac{x^2}{49} + \dfrac{y^2}{36} = 1\).
Focus: \(F(\pm \sqrt{13}, 0)\)
Vertices: \(V(\pm 7, 0)\)
Major axis = \(14\)
Minor axis = \(12\)
Eccentricity: \(e = \dfrac{\sqrt{13}}{7}\)
Latus rectum = \(\dfrac{72}{7}\)
In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
For the ellipse \(\dfrac{x^2}{100} + \dfrac{y^2}{400} = 1\).
Focus: \(F(0, \pm 10\sqrt{3})\)
Vertices: \(V(0, \pm 20)\)
Major axis = \(40\)
Minor axis = \(20\)
Eccentricity: \(e = \dfrac{\sqrt{3}}{2}\)
Latus rectum = \(10\)
In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
For the ellipse \(36x^2 + 4y^2 = 144\).
Focus: \(F(0, \pm 4\sqrt{2})\)
Vertices: \(V(0, \pm 6)\)
Major axis = \(12\)
Minor axis = \(4\)
Eccentricity: \(e = \dfrac{2\sqrt{2}}{3}\)
Latus rectum = \(\dfrac{4}{3}\)
In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
For the ellipse \(16x^2 + y^2 = 16\).
Focus: \(F(0, \pm \sqrt{15})\)
Vertices: \(V(0, \pm 4)\)
Major axis = \(8\)
Minor axis = \(2\)
Eccentricity: \(e = \dfrac{\sqrt{15}}{4}\)
Latus rectum = \(\dfrac{1}{2}\)
In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
For the ellipse \(4x^2 + 9y^2 = 36\).
Focus: \(F(\pm \sqrt{5}, 0)\)
Vertices: \(V(\pm 3, 0)\)
Major axis = \(6\)
Minor axis = \(4\)
Eccentricity: \(e = \dfrac{\sqrt{5}}{3}\)
Latus rectum = \(\dfrac{8}{3}\)
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions.
Vertices \((\pm 5, 0)\) and foci \((\pm 4, 0)\).
\(\dfrac{x^2}{25} + \dfrac{y^2}{9} = 1\)
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions.
Vertices \((0, \pm 13)\) and foci \((0, \pm 5)\).
\(\dfrac{x^2}{144} + \dfrac{y^2}{169} = 1\)
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions.
Vertices \((\pm 6, 0)\) and foci \((\pm 4, 0)\).
\(\dfrac{x^2}{36} + \dfrac{y^2}{20} = 1\)
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions.
Ends of major axis \((\pm 3, 0)\) and ends of minor axis \((0, \pm 2)\).
\(\dfrac{x^2}{9} + \dfrac{y^2}{4} = 1\)
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions.
Ends of major axis \((0, \pm \sqrt{5})\) and ends of minor axis \((\pm 1, 0)\).
\(\dfrac{x^2}{1} + \dfrac{y^2}{5} = 1\)
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions.
Length of major axis \(26\) and foci \((\pm 5, 0)\).
\(\dfrac{x^2}{169} + \dfrac{y^2}{144} = 1\)
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions.
Length of minor axis \(16\) and foci \((0, \pm 6)\).
\(\dfrac{x^2}{64} + \dfrac{y^2}{100} = 1\)
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions.
Foci \((\pm 3, 0)\) with \(a = 4\).
\(\dfrac{x^2}{16} + \dfrac{y^2}{7} = 1\)
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions.
\(b = 3\), \(c = 4\), centre at the origin and foci on the x-axis.
\(\dfrac{x^2}{25} + \dfrac{y^2}{9} = 1\)
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions.
Centre at \((0, 0)\), major axis on the y-axis and passes through the points \((3, 2)\) and \((1, 6)\).
\(\dfrac{x^2}{10} + \dfrac{y^2}{40} = 1\)
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions.
Major axis on the x-axis and passes through the points \((4, 3)\) and \((6, 2)\).
\(x^2 + 4y^2 = 52\) or \(\dfrac{x^2}{52} + \dfrac{y^2}{13} = 1\)