What is 4(x-5)^2+3(y-5)^2=192 ?

The solution to 4(x-5)^2+3(y-5)^2=192 is Ellipse with (h,k)=(5,5),a=4sqrt(3),b=8

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4(x-5)^2+3(y-5)^2=192

4 (x - 5)^{2} + 3 (y - 5)^{2} = 192

(h, k) = (5, 5), a = 43, b = 8

Solution steps

4 (x - 5)^{2} + 3 (y - 5)^{2} = 192

Rewrite

4 (x - 5)^{2} + 3 (y - 5)^{2} = 192

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{( 4 3 ) ^{2}} + \frac{( y - 5 ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, 5), a = 43, b = 8

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (5, 5), b = 8, a = 43

25 x^{2} + y^{2} = 1

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{16} = 1

\frac{( x - 18.093 ) ^{2}}{20} + \frac{( y - 3 ) ^{2}}{21} = 1

\frac{( x - 20 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

\frac{( x + 1 ) ^{2}}{2} + \frac{( y - 6 ) ^{2}}{187} = 1

What is 4(x-5)^2+3(y-5)^2=192 ?
The solution to 4(x-5)^2+3(y-5)^2=192 is Ellipse with (h,k)=(5,5),a=4sqrt(3),b=8