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A tangent to the ellipse  at any point P meet the line x = 0 at a point Q. Let R be the image of Q in the line y = x, then circle whose extremities of a diameter are Q and R passes through a fixed point. The fixed point is
  • a)
    (3, 0)
  • b)
    (5, 0)
  • c)
    (0, 0)
  • d)
    (4, 0)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A tangent to the ellipse at any point P meet the line x = 0 at a point...
Equation of the tangent to the ellipse at P (5 cos θ , 4 sin θ) is 
It meets the line x = 0 at Q (0, 4 cosec θ)
Image of Q in the line y = x is R (4 cosec θ , 0)
∴ Equation of the circle is
X (x – 4 cosec θ) + y(y – 4 cosec θ) = 0
i.e. x2 + y2 – 4 (x + y) cosec θ = 0
∴ each member of the family passes through the intersection of x2 + y2 = 0 and x + y = 0
i.e. the point (0, 0).
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A tangent to the ellipse at any point P meet the line x = 0 at a point Q. Let R be the image of Q in the line y = x, then circle whose extremities of a diameter are Q and R passes through a fixed point. The fixed point isa)(3, 0)b)(5, 0)c)(0, 0)d)(4, 0)Correct answer is option 'C'. Can you explain this answer?
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A tangent to the ellipse at any point P meet the line x = 0 at a point Q. Let R be the image of Q in the line y = x, then circle whose extremities of a diameter are Q and R passes through a fixed point. The fixed point isa)(3, 0)b)(5, 0)c)(0, 0)d)(4, 0)Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A tangent to the ellipse at any point P meet the line x = 0 at a point Q. Let R be the image of Q in the line y = x, then circle whose extremities of a diameter are Q and R passes through a fixed point. The fixed point isa)(3, 0)b)(5, 0)c)(0, 0)d)(4, 0)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tangent to the ellipse at any point P meet the line x = 0 at a point Q. Let R be the image of Q in the line y = x, then circle whose extremities of a diameter are Q and R passes through a fixed point. The fixed point isa)(3, 0)b)(5, 0)c)(0, 0)d)(4, 0)Correct answer is option 'C'. Can you explain this answer?.
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