EllipseMedium
Question
Let tangents drawn from point (0,5) to the ellipse 
= 1 are perpendicular and meet major axis of ellipse at points A & B. A hyperbola ′H′ is drawn whose eccentricity is reciprocal of eccentricity of ellipse & whose foci are points A & B, then-
= 1 are perpendicular and meet major axis of ellipse at points A & B. A hyperbola ′H′ is drawn whose eccentricity is reciprocal of eccentricity of ellipse & whose foci are points A & B, then-Options
A.eccentricity of ellipse is 
B.hyperbola ′H′ is 
= 25
= 25C.C) hyperbola ′H′ is 4x2 - 12y2 = 75
D.Length of latus rectum of ellipse is 
Solution
(0,5) lies on director circle of ellipse i.e.
x2 + y2 = a2 + 5
⇒ a2 = 20
⇒ eccentricity of ellipse is e =
Let tangents are y = mx + 5
∵ c2 = a2m2 + b2 ⇒ 25 = 20m2 + 5 ⇒ m = ± 1
points A & B are (5, 0) & (-5, 0)
for hyperbola ′H′ foci are (±5,0) & e =
′H′ is 4x2 - 12y2 = 75
x2 + y2 = a2 + 5
⇒ a2 = 20
⇒ eccentricity of ellipse is e =
Let tangents are y = mx + 5
∵ c2 = a2m2 + b2 ⇒ 25 = 20m2 + 5 ⇒ m = ± 1
points A & B are (5, 0) & (-5, 0)
for hyperbola ′H′ foci are (±5,0) & e =
′H′ is 4x2 - 12y2 = 75
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