Question

alem: Find the point to which the origin is to be shifted by the translation of axes so as to remove
the first degree terms from the equation
ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, where h2 not equal to ab.​

Answer 1

Answer:

X Axis (4,2)

Step-by-step explanation:

It's the point.. hope it helps.. please mark me the brainliest answer

Answer 2

Answer:

(g/a,f/b) is the point to which the origin is to be shifted by the translation of axes so as to remove the first degree terms from the equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0,

Step-by-step explanation:

ax² + 2hxy + by² + 2gx + 2fy + c = 0,

let orgin is shifted to  (h,k ), then the x=x-h, y=y-k

substituting x and y values in the given equation

a(x-h)²+2h(x-h)(y-k) +b(y-k)²+2g(x-h)+2f(y-k)+c=0

a(x²-2hx+h²)+b(y²+k²-2yk)+2gx-2gh+2fy-2fk+c=0

ax²+by²+x(2g-2ah)+y(2f-2bk)+ah²+bk²-2gh-2fk+c=0

to remove first degree terms,

in the above equation x and y terms should be equal to zero

2g-2ah=0

h=g/a

similarly

2f-2bk=0

k=f/b

Therfore (g/a,f/b) is the point to which the origin is to be shifted by the translation of axes so as to remove the first degree terms from the equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0,