Topic For ellipse (E): \(\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{9} = 1\). Find the coordinates of the point \(M \in \left( E \right)\) such that the length \({F_2}M\) is maximum, given that \({F_2}\)…
Topic The Earth moves around the Sun in an elliptical orbit of which the Sun is the focal point. Given that this ellipse has a semi-major axis \(a \approx 149.598.261\)…
Topic In the coordinate plane Oxy, for the hyperbola the canonical equation is \(\frac{{{x^2}}}{4} – \frac{{{y^2}}}{1} = 1\) a) Determine the coordinates of the vertices, the focal point, the focal…
Topic Write down the canonical equation of the ellipse (E) in each of the following cases: a) The length of the major axis is 6 and the focal point is…
Topic Pluto moves around the Sun in an orbit that is an ellipse with one of the two focal points being the center of the Sun. Given that this ellipse…
Practice Let the hyperbola (H) have a vertex of \({A_1}( – 4;0)\) and a focal length of 10. Write the canonical equation and draw the hyperbola (H). Detailed explanation: Hyperbola…
Topic The first artificial satellite was launched from Earth by the Soviet Union (former) in 1957. The satellite's orbit is an ellipse with the center of the Earth as a…
Contract 8 Let the ellipse (E) have the canonical equation \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^) 2}}} = 1\) \((0 < b < a)\) Consider a circle (C) with center O and radius…
Problem In the coordinate plane Oxy, for the line \(\Delta 😡 = – 5\) and the point \(F\left( { – 4;0} \right)\). Take 3 points \(A\left( { – 3;1} \right),B\left(…
Select a sentence to see the solution faster Contract 5 In the plane, consider the hyperbola (H) as the set of points M such that \(\left| {M{F_1} – M{F_2}} \right|…