What is ((x-1)^2)/(169)+((y-4)^2)/(144)=1 ?

The solution to ((x-1)^2)/(169)+((y-4)^2)/(144)=1 is Ellipse with (h,k)=(1,4),a=13,b=12

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((x-1)^2)/(169)+((y-4)^2)/(144)=1

\frac{( x - 1 ) ^{2}}{169} + \frac{( y - 4 ) ^{2}}{144} = 1

(h, k) = (1, 4), a = 13, b = 12

Solution steps

\frac{( x - 1 ) ^{2}}{169} + \frac{( y - 4 ) ^{2}}{144} = 1

Rewrite

\frac{( x - 1 ) ^{2}}{169} + \frac{( y - 4 ) ^{2}}{144} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 4), a = 13, b = 12

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 4), a = 13, b = 12

9 x^{2} + 25 y^{2} - 18 x - 50 y - 191 = 0

3 x^{2} + 3 y^{2} - 6 y = 0

\frac{( x - 3 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{25} = 1

4 x^{2} - 16 x + 9 y^{2} + 54 y + 61 = 0

9 x^{2} + 16 y^{2} - 18 x + 64 y = 71

What is ((x-1)^2)/(169)+((y-4)^2)/(144)=1 ?
The solution to ((x-1)^2)/(169)+((y-4)^2)/(144)=1 is Ellipse with (h,k)=(1,4),a=13,b=12