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What will be the equation of the normal to the parabola y2 = 3x which is perpendicular to the line y = 2x + 4?
- a)16x + 32y = 27
- b)16x – 32y = 27
- c)16x + 32y = -27
- d)-16x + 32y = 27
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
What will be the equation of the normal to the parabola y2= 3x which i...
Given, y2 = 3x ……….(1) and y = 2x + 4 ……….(2)
Differentiating both sides of (1) with respect to y we get,
2y = 3(dx/dy)
Or dx/dy = 2y/3
Let P (x1, y1) be any point on the parabola (1). Then the slope of the normal to the parabola (1) at point P is
-[dx/dy]P = -2y1/3
If the normal at the point P to the parabola (1) be perpendicular to the line (2) then we must have,
-2y1/3*2 = -1
Since the slope of the line (2) is 2
Or y1 = 3/4
Since the point P(x1, y1) lies on (1) hence,
y12 = 3x1
As, y1 = 3/4, so, x1 = 3/16
Therefore, the required equation of the normal is
y – y1 = -(2y1)/3*(x – x1)
Putting the value of x1 and y1 in the above equation we get,
16x + 32y = 27.
Differentiating both sides of (1) with respect to y we get,
2y = 3(dx/dy)
Or dx/dy = 2y/3
Let P (x1, y1) be any point on the parabola (1). Then the slope of the normal to the parabola (1) at point P is
-[dx/dy]P = -2y1/3
If the normal at the point P to the parabola (1) be perpendicular to the line (2) then we must have,
-2y1/3*2 = -1
Since the slope of the line (2) is 2
Or y1 = 3/4
Since the point P(x1, y1) lies on (1) hence,
y12 = 3x1
As, y1 = 3/4, so, x1 = 3/16
Therefore, the required equation of the normal is
y – y1 = -(2y1)/3*(x – x1)
Putting the value of x1 and y1 in the above equation we get,
16x + 32y = 27.
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What will be the equation of the normal to the parabola y2= 3x which i...
To find the equation of the normal to the parabola that is perpendicular to the line y = 2x - 4, we need to find the slope of the line y = 2x - 4, which is 2.
The slope of the normal to the parabola will be the negative reciprocal of the slope of the line, so the slope of the normal is -1/2.
Now, let's find the coordinates of a point on the parabola. Let's choose x = 1, which gives us y^2 = 3(1) = 3. Taking the positive square root, we get y = √3.
So, a point on the parabola is (1, √3).
Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can write the equation of the normal line as:
y - √3 = (-1/2)(x - 1)
Simplifying the equation, we get:
y - √3 = (-1/2)x + 1/2
Multiplying through by 2 to eliminate the fraction, we get:
2y - 2√3 = -x + 1
Rearranging the terms, we get:
x + 2y = 2√3 + 1
So, the equation of the normal to the parabola y^2 = 3x that is perpendicular to the line y = 2x - 4 is x + 2y = 2√3 + 1.
The slope of the normal to the parabola will be the negative reciprocal of the slope of the line, so the slope of the normal is -1/2.
Now, let's find the coordinates of a point on the parabola. Let's choose x = 1, which gives us y^2 = 3(1) = 3. Taking the positive square root, we get y = √3.
So, a point on the parabola is (1, √3).
Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can write the equation of the normal line as:
y - √3 = (-1/2)(x - 1)
Simplifying the equation, we get:
y - √3 = (-1/2)x + 1/2
Multiplying through by 2 to eliminate the fraction, we get:
2y - 2√3 = -x + 1
Rearranging the terms, we get:
x + 2y = 2√3 + 1
So, the equation of the normal to the parabola y^2 = 3x that is perpendicular to the line y = 2x - 4 is x + 2y = 2√3 + 1.
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What will be the equation of the normal to the parabola y2= 3x which is perpendicular to the line y = 2x + 4?a)16x + 32y = 27b)16x – 32y = 27c)16x + 32y = -27d)-16x + 32y = 27Correct answer is option 'A'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about What will be the equation of the normal to the parabola y2= 3x which is perpendicular to the line y = 2x + 4?a)16x + 32y = 27b)16x – 32y = 27c)16x + 32y = -27d)-16x + 32y = 27Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the equation of the normal to the parabola y2= 3x which is perpendicular to the line y = 2x + 4?a)16x + 32y = 27b)16x – 32y = 27c)16x + 32y = -27d)-16x + 32y = 27Correct answer is option 'A'. Can you explain this answer?.
What will be the equation of the normal to the parabola y2= 3x which is perpendicular to the line y = 2x + 4?a)16x + 32y = 27b)16x – 32y = 27c)16x + 32y = -27d)-16x + 32y = 27Correct answer is option 'A'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about What will be the equation of the normal to the parabola y2= 3x which is perpendicular to the line y = 2x + 4?a)16x + 32y = 27b)16x – 32y = 27c)16x + 32y = -27d)-16x + 32y = 27Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the equation of the normal to the parabola y2= 3x which is perpendicular to the line y = 2x + 4?a)16x + 32y = 27b)16x – 32y = 27c)16x + 32y = -27d)-16x + 32y = 27Correct answer is option 'A'. Can you explain this answer?.
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What will be the equation of the normal to the parabola y2= 3x which is perpendicular to the line y = 2x + 4?a)16x + 32y = 27b)16x – 32y = 27c)16x + 32y = -27d)-16x + 32y = 27Correct answer is option 'A'. Can you explain this answer?, a detailed solution for What will be the equation of the normal to the parabola y2= 3x which is perpendicular to the line y = 2x + 4?a)16x + 32y = 27b)16x – 32y = 27c)16x + 32y = -27d)-16x + 32y = 27Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of What will be the equation of the normal to the parabola y2= 3x which is perpendicular to the line y = 2x + 4?a)16x + 32y = 27b)16x – 32y = 27c)16x + 32y = -27d)-16x + 32y = 27Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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