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The equation of the common tangent to the parabola y2 = 8x and the hyperbola 3x2– y2 = 3 is
  • a)
    2x ± y + 1 = 0
  • b)
    x ± y + 1 = 0
  • c)
    x ± 2y + 1 = 0
  • d)
    x ± y + 2 = 0
Correct answer is option 'A'. Can you explain this answer?
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The equation of the common tangent to the parabola y2= 8x and the hype...

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Explanation:

Equation of Parabola:
- The given equation of the parabola is y^2 = 8x.
- This is a parabola that opens towards the right.

Equation of Hyperbola:
- The given equation of the hyperbola is 3x^2 - y^2 = 3.
- This is a hyperbola that opens towards the x-axis.

Finding the Tangent:
- To find the common tangent to both curves, we need to find the point of tangency.
- Differentiating the equations of the curves, we get:
- For the parabola: dy/dx = 4/y
- For the hyperbola: dy/dx = 2x/2y = x/y
- Equating the derivatives and solving for x and y, we get x = 1, y = ±2.

Equation of Tangent:
- The equation of the tangent to a curve at a point (x1, y1) is given by:
- (y - y1) = m(x - x1), where m is the slope of the tangent.
- Substituting the point of tangency (1, 2) into the equations of the parabola and hyperbola, we get the slope of the tangent as 1/2.
- Therefore, the equation of the common tangent is:
- y - 2 = 1/2(x - 1)
- 2x - y - 3 = 0
- 2x - y + 1 = 0
Therefore, the correct answer is option 'A': 2x ± y + 1 = 0.
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The equation of the common tangent to the parabola y2= 8x and the hyperbola 3x2–y2= 3 isa)2x ± y + 1 = 0b)x ± y + 1 = 0c)x ± 2y + 1 = 0d)x ± y + 2 = 0Correct answer is option 'A'. Can you explain this answer?
Question Description
The equation of the common tangent to the parabola y2= 8x and the hyperbola 3x2–y2= 3 isa)2x ± y + 1 = 0b)x ± y + 1 = 0c)x ± 2y + 1 = 0d)x ± y + 2 = 0Correct answer is option 'A'. 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 The equation of the common tangent to the parabola y2= 8x and the hyperbola 3x2–y2= 3 isa)2x ± y + 1 = 0b)x ± y + 1 = 0c)x ± 2y + 1 = 0d)x ± y + 2 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of the common tangent to the parabola y2= 8x and the hyperbola 3x2–y2= 3 isa)2x ± y + 1 = 0b)x ± y + 1 = 0c)x ± 2y + 1 = 0d)x ± y + 2 = 0Correct answer is option 'A'. Can you explain this answer?.
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