Q$1)$ Write java code to draw the parabola $2^{**}Y=3^{**}(x+100{)}^2-40$ taking symmetry into account and assuming $(200,200)$ is the origin.

Q$2)$ Given the shape with the following points :

$(310,200),(370,200),(370,230),(340,250),(310,230).$

The shape is reflected about the line $Y=x-200.$

Write java program to reflect the shape about the line $.$The program should perform the following:

$1-$ Reflection with three matrices using y$-$axis.

$2-$ Drawing the reflection line.

$3-$ Drawing the shape before and after reflection

$4-$ Printing the composite matrix.

$5-$ Calculating the images of the points after reflection

Q$3)$ Use composition of transformations to find the composite matrix to convert the object With the points $,$:$(-1,-1),(1,-1),(1,1),(-1,1)$ into the object with the points : $(2,4),(4,7),(-2,10),(-4,7)$

Q$4)$

Implement the following method:

Polygon preImagePolygon$($Polygon image $,$ int m$[][])$

m : the transformation matrix

image : the points of the polygon after transformation

The method returns the polygon before the transformation