Diameter of a circle is a.b before deformation.
What will be new form of circle under deformation:
$$x_1 = 2 X_1+{1\over 2}X_2$$
$$x_2 = 2 X_1-{1\over 2}X_2$$
I tried to substitute $$ X_1^2+X_2^2=({a.b\over2})^2$$ using $$x_1+x_2=4X_1$$ and $$x_1-x_2=X_2$$ I ended up with $$17x_1^2+17x_2^2-30x_1x_2=4a^2b^2$$ and it doesn't feel right, can't tell whats the new form after deformation by looking that. Am i on the right track? Searched for a similar example on books and on the internet but couldn't find any.
Hint :
Write $$17x_1^2+17x_2^2-30x_1x_2=4a^2b^2$$ as
$$ \left(\dfrac{x_1-x_0}{h_1}\right)^2+\left(\dfrac{x_2-y_0}{h_2}\right)^2=1 $$
which is possible because $x_1$ and $x_2$ have the same coefficient, and which is an ellipse equation.