Show that if P is a point on an ellipse with foci F1 and F2, directrices d1 and d2 and eccentricity e, then P F1 + P F2 is equal to e times the distance between the directrices.

Q: Find the length of the directrix of an ellipse x2/16 + y2/9 = 1

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Q: the ellipse with 4) Write the the center at (o,o), the vertex at Cos-5) and the distance between the…

A: Given center at (0,0), vertex at (0,-5) the distance between focus and vertex is equal to 2 ⇒focus…

Q: The ellipse with the given equation is centered at x² +9y² + 3x - 18y + 9 = 0 3 9 (²/₁₁) (²17,¹1) 2…

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Q: he area of an ellipse with axes of length 2a and 2b is nab. The percent change in the area when a…

A: We have to find percent change in the area after increasing major axis and minor axis.

Q: Find the equation on the ellipse that has its center at the origin and satisfies the conditions:…

A: We have to find the equation on the ellipse that has its center at the origin and satisfies the…

Q: The graph of x+6xy+ 25y = 16 is an ellipse. Find the coordinates of the points where the ellipse has…

A: see below the answer

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 the equation of the ellipse with the given properties: Vertices at (+25,0) and (0, 164)

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Q: For the ellipse (x-1)^2/16+(y+3)^2/4=1, find the center, vertices, foci co vertices and…

A: The given ellipse equation is (x-1)^2/16+(y+3)^2/4=1 To find the center, vertices, foci co vertices…