JEE Exam > JEE Questions > The common tangents to the circle x2 + y2 = 2...
Start Learning for Free
The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)
- a)3
- b)6
- c)9
- d)15
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x...
Let the tangent to y2 = 8x be y = 
If it is common tangent to parabola and circle, then
is a tangent to x2 + y2 = 2
is a tangent to x2 + y2 = 2
⇒ m4 + m2 – 2 = 0 ⇒ (m2 + 2) (m2 – 1) = 0 ⇒ m = 1 or – 1
∴ Required tangents are y = x + 2 and y = – x – 2
∴ Required tangents are y = x + 2 and y = – x – 2
Most Upvoted Answer
The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x...
Approach:
To find the area of the quadrilateral PQRS, we need to first find the coordinates of points P, Q, R, and S using the given equations of the circle and parabola. Then we can use the distance formula to calculate the lengths of the sides of the quadrilateral and apply the formula for the area of a quadrilateral given the lengths of its sides.
Calculations:
- Finding the coordinates of P and Q:
Since the tangents touch the circle x^2 + y^2 = 2 at points P and Q, the equation of the common tangent can be written as y = mx ± √2(1 + m^2). By substituting this equation in the circle equation, we can find the values of m and subsequently the coordinates of P and Q.
- Finding the coordinates of R and S:
Similarly, for the parabola y^2 = 8x, the equation of the common tangent can be written as y = mx + 4/m. By substituting this equation in the parabola equation, we can find the values of m and subsequently the coordinates of R and S.
- Calculating the lengths of the sides:
Once we have the coordinates of P, Q, R, and S, we can use the distance formula to calculate the lengths of the sides PQ, QR, RS, and SP.
- Calculating the area of the quadrilateral:
Finally, we can use the formula for the area of a quadrilateral given the lengths of its sides, which is given by Area = √((s-a)(s-b)(s-c)(s-d)), where s is the semiperimeter and a, b, c, d are the lengths of the sides. By substituting the lengths of the sides, we can calculate the area of the quadrilateral PQRS.
Therefore, the correct answer is option D) 15.
To find the area of the quadrilateral PQRS, we need to first find the coordinates of points P, Q, R, and S using the given equations of the circle and parabola. Then we can use the distance formula to calculate the lengths of the sides of the quadrilateral and apply the formula for the area of a quadrilateral given the lengths of its sides.
Calculations:
- Finding the coordinates of P and Q:
Since the tangents touch the circle x^2 + y^2 = 2 at points P and Q, the equation of the common tangent can be written as y = mx ± √2(1 + m^2). By substituting this equation in the circle equation, we can find the values of m and subsequently the coordinates of P and Q.
- Finding the coordinates of R and S:
Similarly, for the parabola y^2 = 8x, the equation of the common tangent can be written as y = mx + 4/m. By substituting this equation in the parabola equation, we can find the values of m and subsequently the coordinates of R and S.
- Calculating the lengths of the sides:
Once we have the coordinates of P, Q, R, and S, we can use the distance formula to calculate the lengths of the sides PQ, QR, RS, and SP.
- Calculating the area of the quadrilateral:
Finally, we can use the formula for the area of a quadrilateral given the lengths of its sides, which is given by Area = √((s-a)(s-b)(s-c)(s-d)), where s is the semiperimeter and a, b, c, d are the lengths of the sides. By substituting the lengths of the sides, we can calculate the area of the quadrilateral PQRS.
Therefore, the correct answer is option D) 15.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. Can you explain this answer?
Question Description
The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. 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 common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. 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 common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. Can you explain this answer?.
The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. 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 common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. 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 common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. Can you explain this answer?.
Solutions for The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. 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 common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The common tangents to the circle x2 + y2 = 2 and the parabola y2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is(JEE Adv. 2014)a)3b)6c)9d)15Correct answer is option 'D'. 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!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup