utkarshakash said:Homework Statement
Find equation of the curve on reflection of the ellipse [itex]\dfrac{(x-4)^2}{16} + \dfrac{(y-3)^2}{9} = 1 [/itex] about the line x-y-2=0.
Homework Equations
The Attempt at a Solution
Let the general point be P(4+4cosθ,3+3sinθ). Let the reflected point be (h,k).
[itex]\dfrac{4+4cos \theta + h}{2} - \dfrac{3+3sin \theta + k}{2} - 2 =0[/itex]
I need one more condition so that I can eliminate theta.
The equation of a reflected curve is a mathematical representation of a curve that has been reflected over a given axis. This means that for every point on the original curve, there is a corresponding point on the reflected curve that is the same distance from the axis of reflection.
To find the equation of a reflected curve, you need to first identify the axis of reflection. Then, you can use the properties of reflection to determine the new coordinates of each point on the curve. Finally, you can use these new coordinates to write the equation of the reflected curve in terms of the original equation.
A reflected curve and a translated curve are both transformations of an original curve, but they are different in how they change the position of the curve. A reflected curve is flipped over an axis, while a translated curve is shifted horizontally or vertically.
Yes, a curve can be reflected over any axis, including the x-axis, y-axis, and any line in the coordinate plane. The equation of the reflected curve will change based on the axis of reflection, but the overall shape of the curve will remain the same.
The equation of a reflected curve determines the position of each point on the curve after it has been reflected. This, in turn, affects the overall shape and orientation of the reflected curve. For example, reflecting a parabola over the x-axis will result in a parabola opening in the opposite direction.