What is the center 4x^2+5y^2-2x+78y-83=x-3y+3 ?

The center 4x^2+5y^2-2x+78y-83=x-3y+3 is (3/8 ,-81/10)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

center 4x^2+5y^2-2x+78y-83=x-3y+3

center

4 x^{2} + 5 y^{2} - 2 x + 78 y - 83 = x - 3 y + 3

(\frac{3}{8}, - \frac{81}{10})

Solution steps

4 x^{2} + 5 y^{2} - 2 x + 78 y - 83 = x - 3 y + 3

Rewrite

4 x^{2} + 5 y^{2} - 2 x + 78 y - 83 - x + 3 y - 3 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{3}{8} ) ^{2}}{( \frac{33169}{8 5} ) ^{2}} + \frac{( y - ( - \frac{81}{10} ) ) ^{2}}{( \frac{33169}{20} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{3}{8}, - \frac{81}{10}), a = \frac{33169}{8 5}, b = \frac{33169}{20}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{3}{8}, - \frac{81}{10}), a = \frac{33169}{8 5}, b = \frac{33169}{20}

And the center is:

(\frac{3}{8}, - \frac{81}{10})

135 x^{2} + 256 y^{2} - 34560 = 0

9 x^{2} + 4 y^{2} = 25

9 x^{2} + 25 y^{2} + 108 x - 200 y + 499 = 0

\frac{( x - 5 ) ^{2}}{49} + \frac{( y - 9 ) ^{2}}{25} = 1

4 x^{2} + 9 y^{2} = 25

What is the center 4x^2+5y^2-2x+78y-83=x-3y+3 ?
The center 4x^2+5y^2-2x+78y-83=x-3y+3 is (3/8 ,-81/10)