JEE Exam > JEE Questions > T is a point on the tangent to a parabola y2=...
Start Learning for Free
T is a point on the tangent to a parabola y2 = 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Then
- a)SL = 2 (TN)
- b)3 (SL) = 2 (TN)
- c)SL = TN
- d)2 (SL) = 3 (TN)
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
T is a point on the tangent to a parabola y2= 4ax at its point P. TL a...
D
View all questions of this test
Most Upvoted Answer
T is a point on the tangent to a parabola y2= 4ax at its point P. TL a...
To understand why option 'C' is the correct answer, let's analyze the given situation step by step.
1. Tangent to the Parabola:
Consider a point T on the tangent to the parabola y^2 = 4ax. Let's denote the coordinates of point T as (x1, y1).
2. Point P on the Parabola:
Since T lies on the tangent, it is also the point of contact of the tangent with the parabola. Therefore, the coordinates of point P can be written as (x1, y1^2/4a).
3. Focal Radius SP:
The focal radius SP is the line segment joining the focus S (0, a) and point P (x1, y1^2/4a). Let's calculate the slope of this line segment.
- Slope of SP = (y1^2/4a - a)/(x1 - 0)
= (y1^2 - 4a^2)/(4ax1)
4. Perpendicular TL:
Let TL be the perpendicular from point T to the focal radius SP. Since TL is perpendicular to SP, the product of their slopes will be -1.
- Slope of TL * Slope of SP = -1
- Slope of TL * (y1^2 - 4a^2)/(4ax1) = -1
- Slope of TL = -4ax1/(y1^2 - 4a^2)
5. Directrix of the Parabola:
The equation of the directrix of the parabola y^2 = 4ax is given by x = -a.
6. Perpendicular TN:
Let TN be the perpendicular from point T to the directrix of the parabola. Since TN is perpendicular to the directrix, its slope will be zero.
- Slope of TN = 0
Now, let's compare the lengths of SL and TN.
7. Length of SL:
SL is the distance between the points S (0, a) and L (x1, -a). Using the distance formula, we can calculate the length of SL.
- Length of SL = √[(x1 - 0)^2 + (-a - a)^2]
= √[x1^2 + 4a^2]
8. Length of TN:
TN is the distance between the points T (x1, y1) and N (-a, y1). Using the distance formula, we can calculate the length of TN.
- Length of TN = √[(x1 + a)^2 + (y1 - y1)^2]
= √[(x1 + a)^2]
Now, let's compare the lengths of SL and TN.
9. Comparing Lengths:
We need to compare SL and TN, so let's square both the lengths and simplify the expression.
- (Length of SL)^2 = x1^2 + 4a^2
- (Length of TN)^2 = (x1 + a)^2
10. Simplifying the Expression:
Since we need to compare 2(SL) and 3(TN), let's calculate the values of 2(SL)^2 and 3(TN)^2.
- 2(SL)^2 = 2(x1^2 +
1. Tangent to the Parabola:
Consider a point T on the tangent to the parabola y^2 = 4ax. Let's denote the coordinates of point T as (x1, y1).
2. Point P on the Parabola:
Since T lies on the tangent, it is also the point of contact of the tangent with the parabola. Therefore, the coordinates of point P can be written as (x1, y1^2/4a).
3. Focal Radius SP:
The focal radius SP is the line segment joining the focus S (0, a) and point P (x1, y1^2/4a). Let's calculate the slope of this line segment.
- Slope of SP = (y1^2/4a - a)/(x1 - 0)
= (y1^2 - 4a^2)/(4ax1)
4. Perpendicular TL:
Let TL be the perpendicular from point T to the focal radius SP. Since TL is perpendicular to SP, the product of their slopes will be -1.
- Slope of TL * Slope of SP = -1
- Slope of TL * (y1^2 - 4a^2)/(4ax1) = -1
- Slope of TL = -4ax1/(y1^2 - 4a^2)
5. Directrix of the Parabola:
The equation of the directrix of the parabola y^2 = 4ax is given by x = -a.
6. Perpendicular TN:
Let TN be the perpendicular from point T to the directrix of the parabola. Since TN is perpendicular to the directrix, its slope will be zero.
- Slope of TN = 0
Now, let's compare the lengths of SL and TN.
7. Length of SL:
SL is the distance between the points S (0, a) and L (x1, -a). Using the distance formula, we can calculate the length of SL.
- Length of SL = √[(x1 - 0)^2 + (-a - a)^2]
= √[x1^2 + 4a^2]
8. Length of TN:
TN is the distance between the points T (x1, y1) and N (-a, y1). Using the distance formula, we can calculate the length of TN.
- Length of TN = √[(x1 + a)^2 + (y1 - y1)^2]
= √[(x1 + a)^2]
Now, let's compare the lengths of SL and TN.
9. Comparing Lengths:
We need to compare SL and TN, so let's square both the lengths and simplify the expression.
- (Length of SL)^2 = x1^2 + 4a^2
- (Length of TN)^2 = (x1 + a)^2
10. Simplifying the Expression:
Since we need to compare 2(SL) and 3(TN), let's calculate the values of 2(SL)^2 and 3(TN)^2.
- 2(SL)^2 = 2(x1^2 +
Community Answer
T is a point on the tangent to a parabola y2= 4ax at its point P. TL a...
D
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)Correct answer is option 'C'. Can you explain this answer?
Question Description
T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)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 T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)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 T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)Correct answer is option 'C'. Can you explain this answer?.
T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)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 T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)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 T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)Correct answer is option 'C'. Can you explain this answer?.
Solutions for T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)Correct 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 T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice T is a point on the tangent to a parabola y2= 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Thena)SL = 2 (TN)b)3 (SL) = 2 (TN)c)SL = TNd)2 (SL) = 3 (TN)Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
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!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup