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The Sun does NOT lie at the centre of an ellipse. The Sun is at one of the two foci of an ellipse. Have you ever drawn an ellipse with two pins a piece of string and pencil on a board. Insert the two pins into the board/paper. Loosely loop the string over the pins, and tighten with the edge of a pencil. Keeping the string taught with the pencil you can draw an ellipse. The positions of the two pins are the foci of the ellipse. Astronomically, the Sun lies at one of these pins. This was discovered by the Astronomer , Johannes Kepler, who gave us the law, that the Earth sweeps equal arcs in equal times about the Sun . The other focus may be thought of as a 'blind' focus. Have a look in Wikipedia under 'Johannes Kepler'. NB The plural of the noun 'focus' is 'foci'. 'Focuses' is when the word 'focus' is being used as a verb.
With the equation of an ellipse in the form (x/a)² + (y/b)² = 1 the axes of the ellipse lie on the x and y axes and the foci are √(a² - b²) along the x axis. 9x² + 25y² + 100y - 125 = 0 → (3x)² + 25(y² + 4y + 4 - 4) = 125 → (3x)² +25(y + 2)² - 100 = 125 → (3x)² +25(y + 2)² = 225 → (3x)²/225 + (y + 2)²/9 = 1 → (x/5)² + ((y+2)/3)² = 1 Thus the foci are √(5² - 3²) = √16 = 4 either side of the y-axis, but the y axis has been shifted up by 2, thus the two foci are (-4, -2) and (4, -2).
Vertices and the foci lie on the line x =2 Major axis is parellel to the y-axis b > a Center of the ellipse is the midpoint (h,k) of the vertices (2,2) Equation of the ellipse is (x - (2) )^2 / a^2 + (y - (2) )^2 / b^2 Equation of the ellipse is (x-2)^2 / a^2 + (y-2)^2 / b^2 The distance between the center and one of the vertices is b The distance between(2,2) and (2,4) is 2, so b = 2 The distance between the center and one of the foci is c The distance between(2,2) and (2,1) is 1, so c = 1 Now that we know b and c, we can find a^2 c^2=b^2-a^2 (1)^2=(2)^2-a^2 a^2 = 3 The equation of the ellipse is Equation of the ellipse is (x-2)^2 / 3 + (y-2)^2 / 4 =1
NO!!! The planets do NOT orbit in circles. They orbit the Sun in an ellipsoidal manner. An ellipse has two foci. The Sun lies at one of the foci, the other might be deemed to be a 'blind' focus. The Sun does NOT lie at the centre of the ellipse. Also the satellites(moons) orbit their parent planets in a similar manner. It has also been discovered that the planets in an an ellipsoidal manner. That is as each orbit is completed the planet 'over-shoot' their starting point, and the ellipse does not close . See Johannes Kepler, who gave us the Law of orbiting planets sweeping equal arcs in equal times , in 1602 AD.
No, it may lie outside the body. In case of a circular ring, it is at the centre of the ring which is outside the mass of the ring.
It will always lie on a diameter.
All Planets do not lie inside the asteororid Belt . The answer is False