Transformations of curves questions
Transformations of curves questions
Please solve these questions. Using attached PDF.
Bonus Problems I: Transformations of curves
Complete the parts (a){(d)
Determine if there exists a linear transformation T : R2 ! R2 that transforms a curve
on the left into a curve on the right. If yes, nd the standard matrix of an appropriate
transformation. If no, explain why.
(a) Circle x2 + y2 = 1 ! ellipse x2 4xy + 5y2 = 1
For example, the standard matrix of such a T is
No, there is no such transformation, because
Determine if there exists a linear transformation T : R2 ! R2 that transforms a curve
on the left into a curve on the right. If yes, nd the standard matrix of an appropriate
transformation. If no, explain why.
(b) Circle x2 + y2 = 1 ! hyperbola x2 y2 = 1
For example, the standard matrix of such a T is
No, there is no such transformation, because
Determine if there exists a linear transformation T : R2 ! R2 that transforms a curve
on the left into a curve on the right. If yes, nd the standard matrix of an appropriate
transformation. If no, explain why.
(c) Pair of lines x = 1 ! hyperbola x2 y2 = 1
For example, the standard matrix of such a T is
No, there is no such transformation, because
Determine if there exists a linear transformation T : R2 ! R2 that transforms a curve
on the left into a curve on the right. If yes, nd the standard matrix of an appropriate
transformation. If no, explain why.
(d) Hyperbola x2 y2 = 1 ! hyperbola y2 x2 = 1
For example, the standard matrix of such a T is
No, there is no such transformation, because
