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An ellipse has foci at F1(9, 20) and F2(...

An ellipse has foci at `F_1(9, 20)` and `F_2(49,55)` in the xy-plane and is tangent to the x-axis. Find the length of its major axis.

A

85

B

75

C

65

D

55

Text Solution

Verified by Experts

The correct Answer is:
A

Image of `F_(1)` in tangent (x-axis) is `F'_(1)`. From the property, points `F_(2), P, F'_(1)` are collinear.
`2a = F_(1)P + F_(2)P = F'_(1)P + F_(2)P = F'_(1)F_(2) = 85`
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