`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.

`A(5,3), B(3,-2)`are two fixed points; find the equation to the locus

1.	`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.
Answer» area of triangle`=1/2\|[x_!,y_1,1],[x_2,y_2,1],[x_3,y_3,1]\|` `/_=1/2\|[h,k,1],[5,3,1],[3,-2,1]\|=9` `/_=h(3+2)-k(5-3)+1(-10-9)=18` `5h-2k-19=18` `5h-2k=37` putting h=x,k=y `5x-2y=37`.

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.