JEE Exam > JEE Questions > Statement-1 : An equation of a common tangent...
Start Learning for Free
Statement-1 : An equation of a common tangent to the parabola y2 = 16
x and the ellipse 2x2 + y2 =4 is y = 2x+ 2
Statement-2 : If the line
is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]
x and the ellipse 2x2 + y2 =4 is y = 2x+ 2Statement-2 : If the line
is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]- a)Statement-1 is false, Statement-2 is true.
- b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.
- c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.
- d)Statement-1 is true, statement-2 is false.
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Statement-1 : An equation of a common tangent to the parabola y2 = 16x...
Given equation of ellipse is 2x2 + y2 = 4
Equation of tangent to the ellipse 
...(1)(∵ equation of tangent to the ellipse
is y = mx + c where 
Now, Equation of tangent to the parabola
...(2)(∵ equation of tangent to the parabola y2 = 4ax is
On comparing (1) and (2), we get
Squaring on both the sides, we get 16 (3) = (2m2 + 4) m2
⇒ 48 = m2 (2m2 + 4) ⇒ 2m4 + 4m2 – 48 = 0 ⇒ m4 + 2m2 –24 = 0
⇒ (m2 + 6)(m2 – 4) = 0 ⇒ m2= 4 (∵ m2 ≠ – 6) ⇒ m = ± 2
⇒ Equation of common tangents are
Thus, statement-1 is true.
Statement-2 is obviously true.
⇒ 48 = m2 (2m2 + 4) ⇒ 2m4 + 4m2 – 48 = 0 ⇒ m4 + 2m2 –24 = 0
⇒ (m2 + 6)(m2 – 4) = 0 ⇒ m2= 4 (∵ m2 ≠ – 6) ⇒ m = ± 2
⇒ Equation of common tangents are
Thus, statement-1 is true.
Statement-2 is obviously true.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. Can you explain this answer?
Question Description
Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. 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 Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. Can you explain this answer?.
Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. 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 Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. Can you explain this answer?.
Solutions for Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. 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 Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Statement-1 : An equation of a common tangent to the parabola y2 = 16x and the ellipse 2x2 + y2=4 is y = 2x+ 2Statement-2 : If the line is a common tan gent to the parabola y2 = 16x and the ellipse 2x2 + y2 = 4, then m satisfies m4 + 2m2 = 24 [2012] [2012]a)Statement-1 is false, Statement-2 is true.b)Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.c)Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.d)Statement-1 is true, statement-2 is false.Correct answer is option 'B'. 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup