"WHEN THE ORIGIN IS SHIFTED TO THE POINT (2,3) THE TRANSFORMED EQUATION OF THE CURVE IS Xsquare+3xy-2y square+17x-16xy+17y square=225 find the qriginal equatio of the curve"

Question

"WHEN THE ORIGIN IS SHIFTED TO THE POINT (2,3) THE TRANSFORMED
EQUATION OF THE CURVE IS Xsquare+3xy-2y square+17x-16xy+17y
square=225 find the qriginal equatio of the curve"

Manbar Singh · Accepted Answer

The given equation is:     x2 + 3xy - 2y2 + 17x - 16xy + 17y2 = 225= x2 - 13xy + 15y2 + 17x - 225 = 0Here we want to shift the point 2, 3 to the origin without changing the direction of axes then, we replace x by x - 2 and y by y - 3 in a equation of given curve then the requiredequation is:     x - 22 - 3 x - 2 y - 3 + 15 y - 32 + 17 x - 2 - 225 = 0⇒ x2 + 4 - 4x - 3 xy - 3x - 2y + 6 + 15 y2 + 9 - 6y + 17x - 34 - 225 = 0⇒ x2 + 4 - 4x - 3xy + 9x + 6y - 18 + 15y2 + 135 - 90y + 17x - 259 = 0⇒ x2 - 3xy + 15y2 + 22x - 84y - 138 = 0