In order to eliminate the first degree terms from the equation 4 x2 + 8 xy + 10 y2 - 8 x - 44 y + 14 = 0 the point to which the origin has to be shifted is

Question

In order to eliminate the first degree terms from the equation 4 x2 + 8 xy + 10 y2 - 8 x - 44 y + 14 = 0 the point to which the origin has to be shifted is (A) (-2, 3) (B) (2, -3) (C) (1, -3) (D) (-1, 3)

Tardigrade Admin · Accepted Answer

On comparing the given equation with a x2+2 h x y+b y2+2 g x+2 f y+c=0, we get a=4, h=4, b=10, g=-4, f=-22 and c=14 For removal of first degree terms, shift the origin to ((b g-f h/h2-a b), (a f-g h/h2-a b)) =((-40+88/16-40), (-88+16/16-40)) =((48/-24), (-72/-24))=(-2,3)

Q. In order to eliminate the first degree terms from the equation 4x2+8xy+10y2−8x−44y+14=0 the point to which the origin has to be shifted is

(-2, 3)

(2, -3)

(1, -3)

(-1, 3)

On comparing the given equation with ax2+2hxy+by2+2gx+2fy+c=0, we get a=4,h=4,b=10,g=−4,f=−22 and c=14 For removal of first degree terms, shift the origin to (h2−abbg−fh​,h2−abaf−gh​)=(16−40−40+88​,16−40−88+16​) =(−2448​,−24−72​)=(−2,3)

Q. In order to eliminate the first degree terms from the equation $4 x^{2} + 8 x y + 10 y^{2} - 8 x - 44 y + 14 = 0$ the point to which the origin has to be shifted is