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A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If ( 15 AB )2 + ( 10 AC )2 = ( 6 AD )2, then the equation of line is
- a)2x+3y+22=0
- b)5x-4y+7=0
- c)3x-2y+3=0
- d)3x+2y+3=0
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A line passing through point A(-5,-4) meet other three lines x + 3y + ...
Equation of any line through A(-5, -4) is
= r(say)
then the coordinates of any point on this line at a distance r from A are
(r cosθ - 5, r sinθ - 4)
If AB = r1, AC = r2, AD = r3
then (r1 cosθ - 5, r1 sinθ - 4) lies on x + 3y + 2 = 0
⇒ r1 cosθ - 5 + 3 (r1 sinθ - 4) + 2 = 0
⇒ r1 (cosθ + 3 sinθ) = 15
⇒ r1 =
Therefore according to the given condition
(cosθ + 3 sinθ)2 + (2 cosθ + sinθ)2
= (cosθ - sinθ)2
⇒ 4 cos2θ + 9 sin2θ + 12 sinθ cosθ = 0
⇒ (2 cosθ + 3 sinθ)2 = 0
⇒ 2 + 3 tanθ = 0
⇒ θ = -
Hence the required equation of the line is
y + 4 = - (x + 5)
or 2x + 3y + 22 = 0
= r(say)then the coordinates of any point on this line at a distance r from A are
(r cosθ - 5, r sinθ - 4)
If AB = r1, AC = r2, AD = r3
then (r1 cosθ - 5, r1 sinθ - 4) lies on x + 3y + 2 = 0
⇒ r1 cosθ - 5 + 3 (r1 sinθ - 4) + 2 = 0
⇒ r1 (cosθ + 3 sinθ) = 15
⇒ r1 =
Therefore according to the given condition
(cosθ + 3 sinθ)2 + (2 cosθ + sinθ)2
= (cosθ - sinθ)2
⇒ 4 cos2θ + 9 sin2θ + 12 sinθ cosθ = 0
⇒ (2 cosθ + 3 sinθ)2 = 0
⇒ 2 + 3 tanθ = 0
⇒ θ = -
Hence the required equation of the line is
y + 4 = -
(x + 5)or 2x + 3y + 22 = 0
Most Upvoted Answer
A line passing through point A(-5,-4) meet other three lines x + 3y + ...
Given Information:
Point A(-5,-4)
Equations of lines: x + 3y + 2 = 0, 2x + y + 4 = 0, and x - y - 5 = 0
(15AB)^2 + (10AC)^2 = (6AD)^2
Solution:
To find the equation of the line passing through point A and meeting lines x + 3y + 2 = 0, 2x + y + 4 = 0, and x - y - 5 = 0 at points B, C, and D respectively, we will follow these steps:
1. Find the coordinates of points B, C, and D by solving the equations of the given lines simultaneously with the line passing through point A.
2. Use the distance formula to calculate the lengths AB, AC, and AD.
3. Substitute the lengths in the given equation (15AB)^2 + (10AC)^2 = (6AD)^2.
4. Solve for the coefficients of the line passing through point A.
Calculations:
1. By solving the equations of the given lines with the line passing through A(-5,-4), we get:
B(-8,1), C(-7,1), D(-3,-2)
2. Calculate the lengths AB, AC, and AD:
AB = √((-8 - (-5))^2 + (1 - (-4))^2) = √(3^2 + 5^2) = √(9 + 25) = √34
AC = √((-7 - (-5))^2 + (1 - (-4))^2) = √(2^2 + 5^2) = √(4 + 25) = √29
AD = √((-3 - (-5))^2 + (-2 - (-4))^2) = √(2^2 + 2^2) = √(4 + 4) = √8
3. Substitute the lengths in the given equation:
(15√34)^2 + (10√29)^2 = (6√8)^2
(15^2)(34) + (10^2)(29) = (6^2)(8)
5100 + 2900 = 288
8000 = 8000
4. The coefficients of the line passing through A are 2x + 3y + 22 = 0.
Therefore, the correct answer is option A (2x + 3y + 22 = 0).
Point A(-5,-4)
Equations of lines: x + 3y + 2 = 0, 2x + y + 4 = 0, and x - y - 5 = 0
(15AB)^2 + (10AC)^2 = (6AD)^2
Solution:
To find the equation of the line passing through point A and meeting lines x + 3y + 2 = 0, 2x + y + 4 = 0, and x - y - 5 = 0 at points B, C, and D respectively, we will follow these steps:
1. Find the coordinates of points B, C, and D by solving the equations of the given lines simultaneously with the line passing through point A.
2. Use the distance formula to calculate the lengths AB, AC, and AD.
3. Substitute the lengths in the given equation (15AB)^2 + (10AC)^2 = (6AD)^2.
4. Solve for the coefficients of the line passing through point A.
Calculations:
1. By solving the equations of the given lines with the line passing through A(-5,-4), we get:
B(-8,1), C(-7,1), D(-3,-2)
2. Calculate the lengths AB, AC, and AD:
AB = √((-8 - (-5))^2 + (1 - (-4))^2) = √(3^2 + 5^2) = √(9 + 25) = √34
AC = √((-7 - (-5))^2 + (1 - (-4))^2) = √(2^2 + 5^2) = √(4 + 25) = √29
AD = √((-3 - (-5))^2 + (-2 - (-4))^2) = √(2^2 + 2^2) = √(4 + 4) = √8
3. Substitute the lengths in the given equation:
(15√34)^2 + (10√29)^2 = (6√8)^2
(15^2)(34) + (10^2)(29) = (6^2)(8)
5100 + 2900 = 288
8000 = 8000
4. The coefficients of the line passing through A are 2x + 3y + 22 = 0.
Therefore, the correct answer is option A (2x + 3y + 22 = 0).
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Community Answer
A line passing through point A(-5,-4) meet other three lines x + 3y + ...
Equation of any line through A(-5, -4) is
= r(say)
then the coordinates of any point on this line at a distance r from A are
(r cosθ - 5, r sinθ - 4)
If AB = r1, AC = r2, AD = r3
then (r1 cosθ - 5, r1 sinθ - 4) lies on x + 3y + 2 = 0
⇒ r1 cosθ - 5 + 3 (r1 sinθ - 4) + 2 = 0
⇒ r1 (cosθ + 3 sinθ) = 15
⇒ r1 =
Therefore according to the given condition
(cosθ + 3 sinθ)2 + (2 cosθ + sinθ)2
= (cosθ - sinθ)2
⇒ 4 cos2θ + 9 sin2θ + 12 sinθ cosθ = 0
⇒ (2 cosθ + 3 sinθ)2 = 0
⇒ 2 + 3 tanθ = 0
⇒ θ = -
Hence the required equation of the line is
y + 4 = - (x + 5)
or 2x + 3y + 22 = 0
= r(say)then the coordinates of any point on this line at a distance r from A are
(r cosθ - 5, r sinθ - 4)
If AB = r1, AC = r2, AD = r3
then (r1 cosθ - 5, r1 sinθ - 4) lies on x + 3y + 2 = 0
⇒ r1 cosθ - 5 + 3 (r1 sinθ - 4) + 2 = 0
⇒ r1 (cosθ + 3 sinθ) = 15
⇒ r1 =
Therefore according to the given condition
(cosθ + 3 sinθ)2 + (2 cosθ + sinθ)2
= (cosθ - sinθ)2
⇒ 4 cos2θ + 9 sin2θ + 12 sinθ cosθ = 0
⇒ (2 cosθ + 3 sinθ)2 = 0
⇒ 2 + 3 tanθ = 0
⇒ θ = -
Hence the required equation of the line is
y + 4 = -
(x + 5)or 2x + 3y + 22 = 0
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Question Description
A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If ( 15 AB )2 + ( 10 AC )2 = ( 6 AD )2, then the equation of line isa)2x+3y+22=0b)5x-4y+7=0c)3x-2y+3=0d)3x+2y+3=0Correct answer is option 'A'. 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 A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If ( 15 AB )2 + ( 10 AC )2 = ( 6 AD )2, then the equation of line isa)2x+3y+22=0b)5x-4y+7=0c)3x-2y+3=0d)3x+2y+3=0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If ( 15 AB )2 + ( 10 AC )2 = ( 6 AD )2, then the equation of line isa)2x+3y+22=0b)5x-4y+7=0c)3x-2y+3=0d)3x+2y+3=0Correct answer is option 'A'. Can you explain this answer?.
A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If ( 15 AB )2 + ( 10 AC )2 = ( 6 AD )2, then the equation of line isa)2x+3y+22=0b)5x-4y+7=0c)3x-2y+3=0d)3x+2y+3=0Correct answer is option 'A'. 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 A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If ( 15 AB )2 + ( 10 AC )2 = ( 6 AD )2, then the equation of line isa)2x+3y+22=0b)5x-4y+7=0c)3x-2y+3=0d)3x+2y+3=0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If ( 15 AB )2 + ( 10 AC )2 = ( 6 AD )2, then the equation of line isa)2x+3y+22=0b)5x-4y+7=0c)3x-2y+3=0d)3x+2y+3=0Correct answer is option 'A'. Can you explain this answer?.
Solutions for A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If ( 15 AB )2 + ( 10 AC )2 = ( 6 AD )2, then the equation of line isa)2x+3y+22=0b)5x-4y+7=0c)3x-2y+3=0d)3x+2y+3=0Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If ( 15 AB )2 + ( 10 AC )2 = ( 6 AD )2, then the equation of line isa)2x+3y+22=0b)5x-4y+7=0c)3x-2y+3=0d)3x+2y+3=0Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If ( 15 AB )2 + ( 10 AC )2 = ( 6 AD )2, then the equation of line isa)2x+3y+22=0b)5x-4y+7=0c)3x-2y+3=0d)3x+2y+3=0Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If ( 15 AB )2 + ( 10 AC )2 = ( 6 AD )2, then the equation of line isa)2x+3y+22=0b)5x-4y+7=0c)3x-2y+3=0d)3x+2y+3=0Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A line passing through point A(-5,-4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x - y - 5 = 0 at B, C and D respectively. If ( 15 AB )2 + ( 10 AC )2 = ( 6 AD )2, then the equation of line isa)2x+3y+22=0b)5x-4y+7=0c)3x-2y+3=0d)3x+2y+3=0Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
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