Let tangents drawn from point (0,5) to the ellipse = 1 are perpendicular and meet major axis of elli

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 &#8242;H&#8242; is drawn whose eccentricity is reciprocal of eccentricity of ellipse & whose foci are points A & B, then-

Accepted Answer

(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

Question

Options

Solution

More Ellipse Questions