JEE Exam > JEE Questions > The line y=mx+c touches the parabola x2=4ay i...
Start Learning for Free
The line y=mx+c touches the parabola x2=4ay if
- a)c=-am
- b)c=-am
- c)c=-am2
- d)c=a/m2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)...
Y= mx + c; x²= 4ay
Subst y in the equation of parabola
x²= 4a(mx + c)
x²-4amx-4ac = 0
Since the line touches the parabola at one point The above quadratic will have one root
b²-4ac = 0
b²= 4ac
16a²m² = 4(1)(-4ac)
16a²m²= -16ac
c=-am²
Subst y in the equation of parabola
x²= 4a(mx + c)
x²-4amx-4ac = 0
Since the line touches the parabola at one point The above quadratic will have one root
b²-4ac = 0
b²= 4ac
16a²m² = 4(1)(-4ac)
16a²m²= -16ac
c=-am²
Most Upvoted Answer
The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)...
Y= mx + c; x²= 4ay
Subst y in the equation of parabola
x²= 4a(mx + c)
x²-4amx-4ac = 0
Since the line touches the parabola at one point The above quadratic will have one root
b²-4ac = 0
b²= 4ac
16a²m² = 4(1)(-4ac)
16a²m²= -16ac
c=-am²
Subst y in the equation of parabola
x²= 4a(mx + c)
x²-4amx-4ac = 0
Since the line touches the parabola at one point The above quadratic will have one root
b²-4ac = 0
b²= 4ac
16a²m² = 4(1)(-4ac)
16a²m²= -16ac
c=-am²
Free Test
FREE
| Start Free Test |
Community Answer
The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)...
Understanding the problem:
The given line y = mx + c touches the parabola x^2 = 4ay. We need to determine the relationship between the coefficients m and c.
Key points:
- The equation of the parabola is x^2 = 4ay.
- The equation of the tangent line is y = mx + c.
- The line touches the parabola at a single point.
Strategy:
1. Find the point of tangency between the line and the parabola by solving the system of equations formed by the line and the parabola.
2. Substitute the coordinates of the point of tangency into the equation of the line to determine the relationship between m and c.
Solution:
1. Substituting y = mx + c into the equation of the parabola x^2 = 4ay, we get:
x^2 = 4a(mx + c)
x^2 = 4amx + 4ac
x^2 - 4amx - 4ac = 0
2. Since the line touches the parabola at a single point, the discriminant of this quadratic equation must be zero:
(4am)^2 - 4*(-4a)*(-4ac) = 0
16a^2m^2 - 64ac = 0
16a(m^2 - 4c) = 0
3. For the line to touch the parabola, m^2 - 4c = 0
Therefore, c = m^2/4
Conclusion:
The correct relationship between the coefficients m and c is c = m^2/4, which is given in option C.
The given line y = mx + c touches the parabola x^2 = 4ay. We need to determine the relationship between the coefficients m and c.
Key points:
- The equation of the parabola is x^2 = 4ay.
- The equation of the tangent line is y = mx + c.
- The line touches the parabola at a single point.
Strategy:
1. Find the point of tangency between the line and the parabola by solving the system of equations formed by the line and the parabola.
2. Substitute the coordinates of the point of tangency into the equation of the line to determine the relationship between m and c.
Solution:
1. Substituting y = mx + c into the equation of the parabola x^2 = 4ay, we get:
x^2 = 4a(mx + c)
x^2 = 4amx + 4ac
x^2 - 4amx - 4ac = 0
2. Since the line touches the parabola at a single point, the discriminant of this quadratic equation must be zero:
(4am)^2 - 4*(-4a)*(-4ac) = 0
16a^2m^2 - 64ac = 0
16a(m^2 - 4c) = 0
3. For the line to touch the parabola, m^2 - 4c = 0
Therefore, c = m^2/4
Conclusion:
The correct relationship between the coefficients m and c is c = m^2/4, which is given in option C.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Question Description
The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)c=a/m2Correct 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 The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)c=a/m2Correct 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 The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)c=a/m2Correct answer is option 'C'. Can you explain this answer?.
The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)c=a/m2Correct 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 The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)c=a/m2Correct 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 The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)c=a/m2Correct answer is option 'C'. Can you explain this answer?.
Solutions for The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)c=a/m2Correct 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 The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)c=a/m2Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)c=a/m2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)c=a/m2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)c=a/m2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The line y=mx+c touches the parabola x2=4ay ifa)c=-amb)c=-amc)c=-am2d)c=a/m2Correct 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 to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup