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Conic Sections Ncert Solutions Maths class 11th Maths Class 11th

If a tangent to the ellipse x² + 4y² = 4 meets the tangents at the extremities of its major axis at B and C, then the circle with BC as diameter passes through the point:

Option 1 -

(1, 1)

Option 2 -

(√2, 0)

Option 3 -

(√3, 0)

Option 4 -

(-1, 1)

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 3

Detailed Solution:

Equation of tangent of P (2cosθ, sinθ) is
(cosθ)x + (2sinθ)y = 4
Solving equation of tangent with equation of tangents at major axis ends, i.e. x = -2 and x = 2
For point 'B' (at x=-2):
-2cosθ + 2sinθ y = 4 ⇒ y = (2+cosθ)/sinθ
B (-2, (2+cosθ)/sinθ)
For point 'C' (at x=2):
2cosθ + 2sinθ y = 4 ⇒ y = (2-cosθ)/sinθ
C (2, (2-cosθ)/sinθ)
Now BC is the diameter of circle
Equation of circle: (x+2) (x-2) + (y - (2+cosθ)/sinθ) (y - (2-cosθ)/sinθ) = 0
x²-4 + y² - (4/sinθ)y + (4-cos²θ)/sin²θ

...more

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Slope of axis = $\frac{1}{2}$

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If a tangent to the ellipse x² + 4y² = 4 meets the tangents at the extremities of its major axis at B and C, then the circle with BC as diameter passes through the point:

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