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The parametric coordinates of any point on the parabola y2 = 4ax can be
- a)(at2, 2at)
- b)(at2, –2at)
- c)(asin2t, 2asint)
- d)(asint, 2acost)
Correct answer is option 'A'. Can you explain this answer?
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The parametric coordinates of any point on the parabola y2= 4ax can be...
Parametric coordinates of the parabola y2 = 4ax are (at2, 2at).
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The parametric coordinates of any point on the parabola y2= 4ax can be...
Parametric coordinates of any conic section is used for converting x and y in same variable . here in case of parabola , it can be written as y / 2a = 2x/y = t , we get y= 2at and x = at^2.
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The parametric coordinates of any point on the parabola y2= 4ax can be...
2at)c)(at, 2at)d)(at, at2)
The correct answer is c) (at, 2at).
To find the parametric coordinates of a point on the parabola y^2 = 4ax, we can use the parameter t.
Let's start by solving the equation for x:
x = y^2 / (4a)
Now, substitute y = 2at into the equation:
x = (2at)^2 / (4a)
x = 4a^2t^2 / (4a)
x = at^2
So, the x-coordinate of any point on the parabola is at^2.
Next, substitute x = at^2 back into the equation y^2 = 4ax:
y^2 = 4a(at^2)
y^2 = 4a^2t^3
Take the square root of both sides:
y = 2at
Therefore, the y-coordinate of any point on the parabola is 2at.
Thus, the parametric coordinates of any point on the parabola y^2 = 4ax are (at, 2at).
The correct answer is c) (at, 2at).
To find the parametric coordinates of a point on the parabola y^2 = 4ax, we can use the parameter t.
Let's start by solving the equation for x:
x = y^2 / (4a)
Now, substitute y = 2at into the equation:
x = (2at)^2 / (4a)
x = 4a^2t^2 / (4a)
x = at^2
So, the x-coordinate of any point on the parabola is at^2.
Next, substitute x = at^2 back into the equation y^2 = 4ax:
y^2 = 4a(at^2)
y^2 = 4a^2t^3
Take the square root of both sides:
y = 2at
Therefore, the y-coordinate of any point on the parabola is 2at.
Thus, the parametric coordinates of any point on the parabola y^2 = 4ax are (at, 2at).
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The parametric coordinates of any point on the parabola y2= 4ax can bea)(at2, 2at)b)(at2, –2at)c)(asin2t, 2asint)d)(asint, 2acost)Correct answer is option 'A'. Can you explain this answer?
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