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Equation of the common tangent to y2 = 8x and 3x2 - y2 = 3 is
- a)2x - y +1 = 0
- b)x + 2y - 5 = 0
- c)2x + y - 6 = 0
- d)2x - y + 7 = 0
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Equation of the common tangent to y2 = 8x and 3x2 - y2= 3 isa)2x - y +...
a = 2 and c2 = a2m2 - b2Most Upvoted Answer
Equation of the common tangent to y2 = 8x and 3x2 - y2= 3 isa)2x - y +...
Understanding the Curves
The equations given are:
- y² = 8x: This is a parabola opening to the right with vertex at (0,0).
- 3x² - y² = 3: This can be rewritten as y² = 3x² - 3, representing a hyperbola.
Finding the Common Tangent
To find the common tangent to both curves, we can use the general form of the tangent line:
y = mx + c, where m is the slope, and c is the y-intercept.
Step 1: Tangent to the Parabola
For the parabola y² = 8x:
- The equation of the tangent can be expressed as y = mx + (4/m) since the condition for tangency gives us c = (4/m).
Step 2: Tangent to the Hyperbola
For the hyperbola 3x² - y² = 3:
- The equation of the tangent can be written as y = mx + c. Using the condition for tangency, we derive a relationship between m and c.
Step 3: Equating Conditions
To find the common tangent, we equate the two conditions derived from the parabola and hyperbola. This leads to a quadratic equation in terms of m.
Step 4: Solving the Quadratic
After solving, we can find values of m and corresponding c.
Step 5: Identifying the Correct Option
Testing the linear functions for common tangents, we can verify:
- Option (a) 2x - y + 1 = 0 can be manipulated into the form y = 2x + 1.
When substituting back into the conditions for both curves, it satisfies both equations, confirming it as a common tangent.
Conclusion
Thus, the correct answer is option (a) 2x - y + 1 = 0. This represents a common tangent to both the parabola and hyperbola defined by the equations provided.
The equations given are:
- y² = 8x: This is a parabola opening to the right with vertex at (0,0).
- 3x² - y² = 3: This can be rewritten as y² = 3x² - 3, representing a hyperbola.
Finding the Common Tangent
To find the common tangent to both curves, we can use the general form of the tangent line:
y = mx + c, where m is the slope, and c is the y-intercept.
Step 1: Tangent to the Parabola
For the parabola y² = 8x:
- The equation of the tangent can be expressed as y = mx + (4/m) since the condition for tangency gives us c = (4/m).
Step 2: Tangent to the Hyperbola
For the hyperbola 3x² - y² = 3:
- The equation of the tangent can be written as y = mx + c. Using the condition for tangency, we derive a relationship between m and c.
Step 3: Equating Conditions
To find the common tangent, we equate the two conditions derived from the parabola and hyperbola. This leads to a quadratic equation in terms of m.
Step 4: Solving the Quadratic
After solving, we can find values of m and corresponding c.
Step 5: Identifying the Correct Option
Testing the linear functions for common tangents, we can verify:
- Option (a) 2x - y + 1 = 0 can be manipulated into the form y = 2x + 1.
When substituting back into the conditions for both curves, it satisfies both equations, confirming it as a common tangent.
Conclusion
Thus, the correct answer is option (a) 2x - y + 1 = 0. This represents a common tangent to both the parabola and hyperbola defined by the equations provided.
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Equation of the common tangent to y2 = 8x and 3x2 - y2= 3 isa)2x - y +1 = 0b)x + 2y - 5 = 0c)2x + y - 6 = 0d)2x - y + 7 = 0Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Equation of the common tangent to y2 = 8x and 3x2 - y2= 3 isa)2x - y +1 = 0b)x + 2y - 5 = 0c)2x + y - 6 = 0d)2x - y + 7 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Equation of the common tangent to y2 = 8x and 3x2 - y2= 3 isa)2x - y +1 = 0b)x + 2y - 5 = 0c)2x + y - 6 = 0d)2x - y + 7 = 0Correct answer is option 'A'. Can you explain this answer?.
Equation of the common tangent to y2 = 8x and 3x2 - y2= 3 isa)2x - y +1 = 0b)x + 2y - 5 = 0c)2x + y - 6 = 0d)2x - y + 7 = 0Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Equation of the common tangent to y2 = 8x and 3x2 - y2= 3 isa)2x - y +1 = 0b)x + 2y - 5 = 0c)2x + y - 6 = 0d)2x - y + 7 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Equation of the common tangent to y2 = 8x and 3x2 - y2= 3 isa)2x - y +1 = 0b)x + 2y - 5 = 0c)2x + y - 6 = 0d)2x - y + 7 = 0Correct answer is option 'A'. Can you explain this answer?.
Solutions for Equation of the common tangent to y2 = 8x and 3x2 - y2= 3 isa)2x - y +1 = 0b)x + 2y - 5 = 0c)2x + y - 6 = 0d)2x - y + 7 = 0Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Equation of the common tangent to y2 = 8x and 3x2 - y2= 3 isa)2x - y +1 = 0b)x + 2y - 5 = 0c)2x + y - 6 = 0d)2x - y + 7 = 0Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Equation of the common tangent to y2 = 8x and 3x2 - y2= 3 isa)2x - y +1 = 0b)x + 2y - 5 = 0c)2x + y - 6 = 0d)2x - y + 7 = 0Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Equation of the common tangent to y2 = 8x and 3x2 - y2= 3 isa)2x - y +1 = 0b)x + 2y - 5 = 0c)2x + y - 6 = 0d)2x - y + 7 = 0Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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