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The mirror image of the parabola y2 = 4x in the tangent to the parabola to the point (1,2) is
- a)(x - 1)2 = 4(y + 1)
- b)(x + 1)2 = 4(y + 1)
- c)(x + 1)2 = 4(y - 1)
- d)(x - 1)2 = 4(y - 1)
Correct answer is option 'C'. Can you explain this answer?
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The mirror image of the parabola y2 = 4x in the tangent to the parabol...
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Mirror Image of the Parabola
The given parabola equation is y^2 = 4x. We need to find the mirror image of this parabola with respect to the tangent to the parabola at the point (1,2).
To find the mirror image, we can reflect the given parabola across the tangent line. Let's find the equation of the tangent line first.
Finding the Tangent Line
To find the equation of the tangent line at the point (1,2), we need to find the slope of the tangent.
We differentiate the equation of the parabola with respect to x to find the slope of the tangent at any point on the parabola.
Differentiating y^2 = 4x with respect to x:
2y * dy/dx = 4
dy/dx = 4 / (2y)
dy/dx = 2/y
At the point (1,2), y = 2. Substituting this into the equation, we get:
dy/dx = 2/2 = 1
So, the slope of the tangent at the point (1,2) is 1.
Using the point-slope form of a line, we can write the equation of the tangent line:
y - y1 = m(x - x1)
y - 2 = 1(x - 1)
y = x + 1
Reflecting the Parabola
Now, let's reflect the given parabola across the tangent line.
The mirror image of any point (x, y) with respect to the line y = x + 1 is (y, x).
So, the mirror image of the parabola equation y^2 = 4x with respect to the tangent line is (x - 1)^2 = 4(y - 1).
Therefore, the correct answer is option 'C': (x - 1)^2 = 4(y - 1).
The given parabola equation is y^2 = 4x. We need to find the mirror image of this parabola with respect to the tangent to the parabola at the point (1,2).
To find the mirror image, we can reflect the given parabola across the tangent line. Let's find the equation of the tangent line first.
Finding the Tangent Line
To find the equation of the tangent line at the point (1,2), we need to find the slope of the tangent.
We differentiate the equation of the parabola with respect to x to find the slope of the tangent at any point on the parabola.
Differentiating y^2 = 4x with respect to x:
2y * dy/dx = 4
dy/dx = 4 / (2y)
dy/dx = 2/y
At the point (1,2), y = 2. Substituting this into the equation, we get:
dy/dx = 2/2 = 1
So, the slope of the tangent at the point (1,2) is 1.
Using the point-slope form of a line, we can write the equation of the tangent line:
y - y1 = m(x - x1)
y - 2 = 1(x - 1)
y = x + 1
Reflecting the Parabola
Now, let's reflect the given parabola across the tangent line.
The mirror image of any point (x, y) with respect to the line y = x + 1 is (y, x).
So, the mirror image of the parabola equation y^2 = 4x with respect to the tangent line is (x - 1)^2 = 4(y - 1).
Therefore, the correct answer is option 'C': (x - 1)^2 = 4(y - 1).
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The mirror image of the parabola y2 = 4x in the tangent to the parabola to the point (1,2) isa)(x - 1)2 = 4(y + 1)b)(x + 1)2 = 4(y + 1)c)(x +1)2 = 4(y -1)d)(x - 1)2 = 4(y -1)Correct answer is option 'C'. 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 mirror image of the parabola y2 = 4x in the tangent to the parabola to the point (1,2) isa)(x - 1)2 = 4(y + 1)b)(x + 1)2 = 4(y + 1)c)(x +1)2 = 4(y -1)d)(x - 1)2 = 4(y -1)Correct answer is option 'C'. 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 mirror image of the parabola y2 = 4x in the tangent to the parabola to the point (1,2) isa)(x - 1)2 = 4(y + 1)b)(x + 1)2 = 4(y + 1)c)(x +1)2 = 4(y -1)d)(x - 1)2 = 4(y -1)Correct answer is option 'C'. Can you explain this answer?.
The mirror image of the parabola y2 = 4x in the tangent to the parabola to the point (1,2) isa)(x - 1)2 = 4(y + 1)b)(x + 1)2 = 4(y + 1)c)(x +1)2 = 4(y -1)d)(x - 1)2 = 4(y -1)Correct answer is option 'C'. 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 mirror image of the parabola y2 = 4x in the tangent to the parabola to the point (1,2) isa)(x - 1)2 = 4(y + 1)b)(x + 1)2 = 4(y + 1)c)(x +1)2 = 4(y -1)d)(x - 1)2 = 4(y -1)Correct answer is option 'C'. 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 mirror image of the parabola y2 = 4x in the tangent to the parabola to the point (1,2) isa)(x - 1)2 = 4(y + 1)b)(x + 1)2 = 4(y + 1)c)(x +1)2 = 4(y -1)d)(x - 1)2 = 4(y -1)Correct answer is option 'C'. Can you explain this answer?.
Solutions for The mirror image of the parabola y2 = 4x in the tangent to the parabola to the point (1,2) isa)(x - 1)2 = 4(y + 1)b)(x + 1)2 = 4(y + 1)c)(x +1)2 = 4(y -1)d)(x - 1)2 = 4(y -1)Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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