If the axes are shifted to the point `(1,-2)`without rotation, what do the following equations become?`2x^2+y^2-4x+4y=0``y^2-4x+4y+8=0`

If the axes are shifted to the point `(1,-2)`without rotation, what do

1.	If the axes are shifted to the point `(1,-2)`without rotation, what do the following equations become?`2x^2+y^2-4x+4y=0``y^2-4x+4y+8=0`
Answer» First equation `2x^2+y^2-4x+4y=0` `2(x-1)^2+(y+2)^2-4(x-1)+4(y+2)=0` `2(x^2+1-2x)+y^2+4+4y-4x+4+4y+8=0` `2x^2+2-2x+y^2+4-4y-4x+4+4y+8=0` `2x^2+y^2-6x+8y+18=0` `y^2-4x+4y+8=0` `y^2+8y-4x+24=0`.

A point moves so that the sum of its distances from `(a e ,0)a n d(-a e ,0)`is `2a ,`prove that the equation to its locus is `(x^2)/(a^2)+(y^2)/(b^2)=1`, where `b^2=a^2(1-e^2)dot`
Find the point to which the origin should be shifted so that theequation `y^2-6y-4x+13=0`is transformed to the form `y^2+A x=0.`
If the axes are shifted to the point `(1,-2)`without rotation, what do the following equations become?`2x^2+y^2-4x+4y=0``y^2-4x+4y+8=0`
Find the locus of a point, such that the join of `(-5,1)a n d(3,2)`subtends a right angle at the moving point.
Find the equation of the locus of a point which moves such that theratio of its distances from `(2,0)a n d(1,3)`is `5: 4.`
`A(5,3), B(3,-2)`are two fixed points; find the equation to the locus of a point `P`which moves so that the area of the triangle `P A B`is 9 units.