What is 1/4 (x-2)^2+1/16 (y+7)^2=1 ?

The solution to 1/4 (x-2)^2+1/16 (y+7)^2=1 is Ellipse with (h,k)=(2,-7),a=2,b=4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

1/4 (x-2)^2+1/16 (y+7)^2=1

\frac{1}{4} (x - 2)^{2} + \frac{1}{16} (y + 7)^{2} = 1

(h, k) = (2, - 7), a = 2, b = 4

Solution steps

\frac{1}{4} (x - 2)^{2} + \frac{1}{16} (y + 7)^{2} = 1

Rewrite

\frac{1}{4} (x - 2)^{2} + \frac{1}{16} (y + 7)^{2} = 1

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 7 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 7), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 7), b = 4, a = 2

4 = x^{2} + 9 y^{2}

1 x^{2} + 3 y^{2} + 9 x + 9 y - 12 = 0

\frac{y ^{2}}{4} + \frac{x ^{2}}{16} = 1

9 x^{2} + 4 y^{2} + 8 x + 48 y = - 117

2 x^{2} + 9 y^{2} = 18

What is 1/4 (x-2)^2+1/16 (y+7)^2=1 ?
The solution to 1/4 (x-2)^2+1/16 (y+7)^2=1 is Ellipse with (h,k)=(2,-7),a=2,b=4