What is (x^2)/k+(y^2)/(4+k)=1 ?

The solution to (x^2)/k+(y^2)/(4+k)=1 is Ellipse with (h,k)=(0,0),a=sqrt(k),b=sqrt(4+k)

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(x^2)/k+(y^2)/(4+k)=1

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

(h, k) = (0, 0), a = k, b = 4 + k

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( k ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 4 + k ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = k, b = 4 + k

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = k, b = 4 + k

\frac{( x + 1 ) ^{2}}{64} + \frac{( y - 5 ) ^{2}}{9} = 1

\frac{( ( x - 4 ) ^{2} )}{36} + \frac{( ( y - 2 ) ^{2} )}{9} = 1

9 x^{2} + 16 y^{2} - 90 x - 160 y + 481 = 0

16 x^{2} + 49 y^{2} = 25

2 x^{2} + y^{2} + 8 y + 14 = 0

What is (x^2)/k+(y^2)/(4+k)=1 ?
The solution to (x^2)/k+(y^2)/(4+k)=1 is Ellipse with (h,k)=(0,0),a=sqrt(k),b=sqrt(4+k)