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Area of the triangle formed by the line x + y = 3 and angle bisectors of the pair of straight lines x2 – y2 + 2y =1 is
- a)2 sq. units
- b)4 sq. units
- c)6 sq. units
- d)8 sq. units
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Area of the triangle formed by the line x + y = 3 and angle bisectors ...
Y2 + 3x + 3y = 0 can be found using the following steps:
1. Find the equations of the angle bisectors of the given pair of straight lines.
The equation of the first line is x2 + y2 + 3x + 3y = 0. By completing the square, we can rewrite it as (x + 3/2)2 + (y + 3/2)2 = 9/2. This is the equation of a circle with center (-3/2, -3/2) and radius √(9/2).
The equation of the second line is x2 + y2 - 3x + 3y = 0. By completing the square, we can rewrite it as (x - 3/2)2 + (y + 3/2)2 = 9/2. This is also the equation of a circle with center (3/2, -3/2) and radius √(9/2).
The angle bisector of these two lines is the line that passes through the intersection points of the two circles. To find these points, we can solve the system of equations:
(x + 3/2)2 + (y + 3/2)2 = 9/2
(x - 3/2)2 + (y + 3/2)2 = 9/2
Subtracting the second equation from the first, we get:
4x = 0
x = 0
Substituting x = 0 into either equation, we get:
y = -3/2 ± √(9/2)
So the intersection points are (0, -3/2 + √(9/2)) and (0, -3/2 - √(9/2)).
The angle bisector passing through (0, -3/2 + √(9/2)) has a slope of -1, since it bisects the acute angle between the two lines. Its equation is y = -x - 3/2 + √(9/2).
The angle bisector passing through (0, -3/2 - √(9/2)) also has a slope of -1, and its equation is y = -x - 3/2 - √(9/2).
2. Find the vertices of the triangle formed by these three lines.
The three lines intersect at three points. To find these points, we can solve the system of equations:
x y = 3
y = -x - 3/2 + √(9/2)
y = -x - 3/2 - √(9/2)
Substituting the second equation into the first, we get:
x(-x - 3/2 + √(9/2)) = 3
-x2 - 3/2x + √(9/2)x - 3 = 0
x2 + 3/2x - √(9/2)x + 3 = 0
Using the quadratic formula, we get:
x = (-3/2 ± √(45/2))/2
Substituting these values of x into either of the other two equations, we get:
y = (-3 ± √
1. Find the equations of the angle bisectors of the given pair of straight lines.
The equation of the first line is x2 + y2 + 3x + 3y = 0. By completing the square, we can rewrite it as (x + 3/2)2 + (y + 3/2)2 = 9/2. This is the equation of a circle with center (-3/2, -3/2) and radius √(9/2).
The equation of the second line is x2 + y2 - 3x + 3y = 0. By completing the square, we can rewrite it as (x - 3/2)2 + (y + 3/2)2 = 9/2. This is also the equation of a circle with center (3/2, -3/2) and radius √(9/2).
The angle bisector of these two lines is the line that passes through the intersection points of the two circles. To find these points, we can solve the system of equations:
(x + 3/2)2 + (y + 3/2)2 = 9/2
(x - 3/2)2 + (y + 3/2)2 = 9/2
Subtracting the second equation from the first, we get:
4x = 0
x = 0
Substituting x = 0 into either equation, we get:
y = -3/2 ± √(9/2)
So the intersection points are (0, -3/2 + √(9/2)) and (0, -3/2 - √(9/2)).
The angle bisector passing through (0, -3/2 + √(9/2)) has a slope of -1, since it bisects the acute angle between the two lines. Its equation is y = -x - 3/2 + √(9/2).
The angle bisector passing through (0, -3/2 - √(9/2)) also has a slope of -1, and its equation is y = -x - 3/2 - √(9/2).
2. Find the vertices of the triangle formed by these three lines.
The three lines intersect at three points. To find these points, we can solve the system of equations:
x y = 3
y = -x - 3/2 + √(9/2)
y = -x - 3/2 - √(9/2)
Substituting the second equation into the first, we get:
x(-x - 3/2 + √(9/2)) = 3
-x2 - 3/2x + √(9/2)x - 3 = 0
x2 + 3/2x - √(9/2)x + 3 = 0
Using the quadratic formula, we get:
x = (-3/2 ± √(45/2))/2
Substituting these values of x into either of the other two equations, we get:
y = (-3 ± √
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Community Answer
Area of the triangle formed by the line x + y = 3 and angle bisectors ...
x2 – y2 + 2y = 1
⇒ x = ±( y - 1)
Bisectors of above line are x = 0 & y = 1
So area between x = 0, y = 1 & x + y = 3 is shaded Region shown in figure.
Area = ½ × 2 × 2 = 2 sq. units
⇒ x = ±( y - 1)
Bisectors of above line are x = 0 & y = 1
So area between x = 0, y = 1 & x + y = 3 is shaded Region shown in figure.
Area = ½ × 2 × 2 = 2 sq. units
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Area of the triangle formed by the line x + y = 3 and angle bisectors of the pair of straight lines x2 – y2 + 2y =1 isa)2 sq. unitsb)4 sq. unitsc)6 sq. unitsd)8 sq. unitsCorrect answer is option 'A'. Can you explain this answer?
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Area of the triangle formed by the line x + y = 3 and angle bisectors of the pair of straight lines x2 – y2 + 2y =1 isa)2 sq. unitsb)4 sq. unitsc)6 sq. unitsd)8 sq. unitsCorrect answer is option 'A'. 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 Area of the triangle formed by the line x + y = 3 and angle bisectors of the pair of straight lines x2 – y2 + 2y =1 isa)2 sq. unitsb)4 sq. unitsc)6 sq. unitsd)8 sq. unitsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Area of the triangle formed by the line x + y = 3 and angle bisectors of the pair of straight lines x2 – y2 + 2y =1 isa)2 sq. unitsb)4 sq. unitsc)6 sq. unitsd)8 sq. unitsCorrect answer is option 'A'. Can you explain this answer?.
Area of the triangle formed by the line x + y = 3 and angle bisectors of the pair of straight lines x2 – y2 + 2y =1 isa)2 sq. unitsb)4 sq. unitsc)6 sq. unitsd)8 sq. unitsCorrect answer is option 'A'. 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 Area of the triangle formed by the line x + y = 3 and angle bisectors of the pair of straight lines x2 – y2 + 2y =1 isa)2 sq. unitsb)4 sq. unitsc)6 sq. unitsd)8 sq. unitsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Area of the triangle formed by the line x + y = 3 and angle bisectors of the pair of straight lines x2 – y2 + 2y =1 isa)2 sq. unitsb)4 sq. unitsc)6 sq. unitsd)8 sq. unitsCorrect answer is option 'A'. Can you explain this answer?.
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