The centre of the ellipse 9x2 + 2 5y2 - 18x- 100y - 116 = 0 is

Question

The centre of the ellipse 9x2 + 2 5y2 - 18x- 100y - 116 = 0 is (A) (1,1) (B) (-1 ,2 ) (C) (1,2) (D) (2,2)

Tardigrade Admin · Accepted Answer

Given equation of ellipse is 9 x2+25y2-18x-100y-116=0 ⇒ 9(x2-2x)+25(y2-4y)-116=0 ⇒ 9(x2-2x+1)+25(y2-4y+4)-100-9-116=0 ⇒ 9(x-1)2+25(y-2)2=225 ∴ Centre (1,2).

Q. The centre of the ellipse
$9 x^{2} + 25 y^{2} - 18 x - 100 y - 116 = 0$ is

$(1, 1)$

$(- 1, 2)$

$(1, 2)$

$(2, 2)$

Given equation of ellipse is
$9 x^{2} + 25 y^{2} - 18 x - 100 y - 116 = 0$
$\Rightarrow 9 (x^{2} - 2 x) + 25 (y^{2} - 4 y) - 116 = 0$
$\Rightarrow 9 (x^{2} - 2 x + 1) + 25 (y^{2} - 4 y + 4) - 100 - 9 - 116 = 0$
$\Rightarrow 9 (x - 1)^{2} + 25 (y - 2)^{2} = 225$
$∴$ Centre $(1, 2)$ .

Q. The centre of the ellipse 9x2+25y2−18x−100y−116=0 is

(1,1)

(−1,2)

(1,2)

(2,2)