Find the vertices of the ellipse given by
$16 x ^ { 2 } + 9 y ^ { 2 } + 160 x - 18 y + 265 = 0 .$
A) $( 5,3 ) , ( 5 , - 5 )$
B) $( - 2,1 ) , ( - 2,1 )$
C) $( 5,4 ) , ( 5 , - 2 )$
D) $( - 1,1 ) , ( - 1,1 )$
E) $( - 5,5 ) , ( - 5 , - 3 )$

Question

Find the vertices of the ellipse given by 
$16 x ^ { 2 } + 9 y ^ { 2 } + 160 x - 18 y + 265 = 0 .$
A) $( 5,3 ) , ( 5 , - 5 )$
B) $( - 2,1 ) , ( - 2,1 )$
C) $( 5,4 ) , ( 5 , - 2 )$
D) $( - 1,1 ) , ( - 1,1 )$
E) $( - 5,5 ) , ( - 5 , - 3 )$

Quizplus · Accepted Answer

To find the vertices, first rewrite the equation in standard form by completing the square. The given equation is $16(x^2 + 10x) + 9(y^2 - 2y) = -265$. Completing the square gives $(x+5)^2$ and $(y-1)^2$. The equation becomes $\frac{(x+5)^2}{9} + \frac{(y-1)^2}{16} = 1$, which is an ellipse centered at $(-5, 1)$ with semi-major axis 4 along the y-axis and semi-minor axis 3 along the x-axis. The vertices are $(-5, 1+4)$ and $(-5, 1-4)$, which are $(-5, 5)$ and $(-5, -3)$.

Find the Vertices of the Ellipse Given By 16x2+9y2+160x−18y+265=0.16 x ^ { 2 } + 9 y ^ { 2 } + 160 x - 18 y + 265 = 0 .16x2+9y2+160x−18y+265=0.

Find the Vertices of the Ellipse Given By $16 x ^ { 2 } + 9 y ^ { 2 } + 160 x - 18 y + 265 = 0 .$