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Two mutually perpendicular straight lines through the origin form an isosceles triangle with the line 2x y=5. Then area of the triangle?
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Two mutually perpendicular straight lines through the origin form an i...
Solution:
Given:
- Two mutually perpendicular straight lines through the origin form an isosceles triangle with the line 2x y=5.
To find:
- The area of the triangle.
Approach:
- Let the two perpendicular lines be y = mx and x = my.
- Let P and Q be the points of intersection of the two lines.
- Let R be the point of intersection of the line 2x y=5 and the line y = mx.
Calculation:
- Since the two perpendicular lines are isosceles, the distance from the origin to P and Q is equal.
- Therefore, OP = OQ.
- Using the distance formula, we get (m^2 + 1)^(1/2) |PQ| = 2 |PR|.
- Also, PR = (2/ (m^2 + 1)^(1/2)) (5 / (2^2 + m^2)^(1/2)).
- The area of the triangle can be found as (1/2) |PQ| |PR|.
- On substituting the values of |PQ| and |PR|, we get the area of the triangle as 5 / 2.
Answer:
- Therefore, the area of the triangle is 5 / 2.
Community Answer
Two mutually perpendicular straight lines through the origin form an i...
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Two mutually perpendicular straight lines through the origin form an isosceles triangle with the line 2x y=5. Then area of the triangle?
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Two mutually perpendicular straight lines through the origin form an isosceles triangle with the line 2x y=5. Then area of the triangle? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two mutually perpendicular straight lines through the origin form an isosceles triangle with the line 2x y=5. Then area of the triangle? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two mutually perpendicular straight lines through the origin form an isosceles triangle with the line 2x y=5. Then area of the triangle?.
Two mutually perpendicular straight lines through the origin form an isosceles triangle with the line 2x y=5. Then area of the triangle? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two mutually perpendicular straight lines through the origin form an isosceles triangle with the line 2x y=5. Then area of the triangle? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two mutually perpendicular straight lines through the origin form an isosceles triangle with the line 2x y=5. Then area of the triangle?.
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