JEE Exam > JEE Questions > If the liney=xis a tangent to the parabolay=a...
Start Learning for Free
If the line y=x is a tangent to the parabola y=ax2+bx+c at the point (1,1) and the curve passes through (−1,0), then
- a)a=b=−1, c=3
- b)a=b=1/2, c=0
- c)a=c=1/4, b=1/2
- d)a=0, b=c=1/2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)a...
Explanation:
Given Conditions:
- The line y = x is a tangent to the parabola y = ax^2 + bx + c at the point (1,1).
- The curve passes through (-1,0).
Using the tangent condition:
- Since the line y = x is a tangent to the parabola y = ax^2 + bx + c at the point (1,1), the slope of the tangent at this point should be equal to 1 (slope of the line y = x).
- The derivative of y = ax^2 + bx + c is y' = 2ax + b.
- At x = 1, the derivative should be equal to 1. So, 2a + b = 1.
Using the point condition:
- Since the curve passes through (-1,0), substituting x = -1 and y = 0 in the equation of the parabola gives 0 = a(-1)^2 + b(-1) + c.
- This simplifies to a - b + c = 0.
Solving the equations:
- From the tangent condition, we have 2a + b = 1.
- From the point condition, we have a - b + c = 0.
- Substituting a = c/4 into the equations above, we get a = c = 1/4 and b = 1/2.
Final Answer:
- Therefore, the correct values for a, b, and c are a = c = 1/4 and b = 1/2, which corresponds to option 'C'.
Given Conditions:
- The line y = x is a tangent to the parabola y = ax^2 + bx + c at the point (1,1).
- The curve passes through (-1,0).
Using the tangent condition:
- Since the line y = x is a tangent to the parabola y = ax^2 + bx + c at the point (1,1), the slope of the tangent at this point should be equal to 1 (slope of the line y = x).
- The derivative of y = ax^2 + bx + c is y' = 2ax + b.
- At x = 1, the derivative should be equal to 1. So, 2a + b = 1.
Using the point condition:
- Since the curve passes through (-1,0), substituting x = -1 and y = 0 in the equation of the parabola gives 0 = a(-1)^2 + b(-1) + c.
- This simplifies to a - b + c = 0.
Solving the equations:
- From the tangent condition, we have 2a + b = 1.
- From the point condition, we have a - b + c = 0.
- Substituting a = c/4 into the equations above, we get a = c = 1/4 and b = 1/2.
Final Answer:
- Therefore, the correct values for a, b, and c are a = c = 1/4 and b = 1/2, which corresponds to option 'C'.
Free Test
FREE
| Start Free Test |
Community Answer
If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)a...
The correct option is C
a=c=1/4, b=1/2
y=x is a tangent
∴ slopes are equal.
dy/dx=2ax+b
⇒1=2a+b at (1,1)⋯(1)
Also, the parabola passes through (1,1)
⇒a+b+c=1⋯(2)
The parabola passes through (−1,0)
⇒0=a−b+c⋯(3)
Solving (1),(2),(3), we get -
∴a=c=1/4
and b=1/2
a=c=1/4, b=1/2
y=x is a tangent
∴ slopes are equal.
dy/dx=2ax+b
⇒1=2a+b at (1,1)⋯(1)
Also, the parabola passes through (1,1)
⇒a+b+c=1⋯(2)
The parabola passes through (−1,0)
⇒0=a−b+c⋯(3)
Solving (1),(2),(3), we get -
∴a=c=1/4
and b=1/2
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Question Description
If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)and the curve passes through(−1,0), thena)a=b=−1, c=3b)a=b=1/2, c=0c)a=c=1/4, b=1/2d)a=0, b=c=1/2Correct answer is option 'C'. 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 If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)and the curve passes through(−1,0), thena)a=b=−1, c=3b)a=b=1/2, c=0c)a=c=1/4, b=1/2d)a=0, b=c=1/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)and the curve passes through(−1,0), thena)a=b=−1, c=3b)a=b=1/2, c=0c)a=c=1/4, b=1/2d)a=0, b=c=1/2Correct answer is option 'C'. Can you explain this answer?.
If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)and the curve passes through(−1,0), thena)a=b=−1, c=3b)a=b=1/2, c=0c)a=c=1/4, b=1/2d)a=0, b=c=1/2Correct answer is option 'C'. 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 If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)and the curve passes through(−1,0), thena)a=b=−1, c=3b)a=b=1/2, c=0c)a=c=1/4, b=1/2d)a=0, b=c=1/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)and the curve passes through(−1,0), thena)a=b=−1, c=3b)a=b=1/2, c=0c)a=c=1/4, b=1/2d)a=0, b=c=1/2Correct answer is option 'C'. Can you explain this answer?.
Solutions for If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)and the curve passes through(−1,0), thena)a=b=−1, c=3b)a=b=1/2, c=0c)a=c=1/4, b=1/2d)a=0, b=c=1/2Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)and the curve passes through(−1,0), thena)a=b=−1, c=3b)a=b=1/2, c=0c)a=c=1/4, b=1/2d)a=0, b=c=1/2Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)and the curve passes through(−1,0), thena)a=b=−1, c=3b)a=b=1/2, c=0c)a=c=1/4, b=1/2d)a=0, b=c=1/2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)and the curve passes through(−1,0), thena)a=b=−1, c=3b)a=b=1/2, c=0c)a=c=1/4, b=1/2d)a=0, b=c=1/2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)and the curve passes through(−1,0), thena)a=b=−1, c=3b)a=b=1/2, c=0c)a=c=1/4, b=1/2d)a=0, b=c=1/2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the liney=xis a tangent to the parabolay=ax2+bx+cat the point(1,1)and the curve passes through(−1,0), thena)a=b=−1, c=3b)a=b=1/2, c=0c)a=c=1/4, b=1/2d)a=0, b=c=1/2Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily