What is ((x-4)^2)/(24)+((y-2)^2)/(49)=1 ?

The solution to ((x-4)^2)/(24)+((y-2)^2)/(49)=1 is Ellipse with (h,k)=(4,2),a=2sqrt(6),b=7

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((x-4)^2)/(24)+((y-2)^2)/(49)=1

\frac{( x - 4 ) ^{2}}{24} + \frac{( y - 2 ) ^{2}}{49} = 1

(h, k) = (4, 2), a = 26, b = 7

Solution steps

\frac{( x - 4 ) ^{2}}{24} + \frac{( y - 2 ) ^{2}}{49} = 1

Rewrite

\frac{( x - 4 ) ^{2}}{24} + \frac{( y - 2 ) ^{2}}{49} = 1

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{( 2 6 ) ^{2}} + \frac{( y - 2 ) ^{2}}{7 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, 2), a = 26, b = 7

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, 2), b = 7, a = 26

5 x^{2} + 2 y^{2} - 10 x + 18 y - 10 = 0

\frac{x ^{2} + y ^{2} - x}{2 x - x ^{2} - y ^{2}} > 0

(x - 2)^{2} + 9 (y - 1)^{2} = 9

16 x^{2} + 32 x + 9 y^{2} + 72 y + 16 = 0

x^{2} + y^{2} = 12 y

What is ((x-4)^2)/(24)+((y-2)^2)/(49)=1 ?
The solution to ((x-4)^2)/(24)+((y-2)^2)/(49)=1 is Ellipse with (h,k)=(4,2),a=2sqrt(6),b=7