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.`

Find the point to which the origin should be shifted so that theequati

1.	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.`
Answer» `y^2+Ax=0` `y^2-6y+(3^2-3^2)-4x+13=0` `(y-3)^2+4-4x=0` `(y-3)^2+4(1-x)=0` `(y-3)^2-4(x-1)=0` `y^2+Ax=0` `A=-4`.`y-3=0` `y=3` `x-1=0` `x=1` Point(1,3).

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.