What is 36x^2+4y^2-49=0 ?

The solution to 36x^2+4y^2-49=0 is Ellipse with (h,k)=(0,0),a= 7/6 ,b= 7/2

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36x^2+4y^2-49=0

36 x^{2} + 4 y^{2} - 49 = 0

(h, k) = (0, 0), a = \frac{7}{6}, b = \frac{7}{2}

Solution steps

36 x^{2} + 4 y^{2} - 49 = 0

Rewrite

36 x^{2} + 4 y^{2} - 49 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{7}{6} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{7}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{7}{6}, b = \frac{7}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{7}{2}, a = \frac{7}{6}

9 x^{2} + 4 y^{2} + 72 x - 8 y - 176 = 0

x^{2} + 4 y + y^{2} = 0

\frac{( x - 3 ) ^{2}}{12} + \frac{( y + 4 ) ^{2}}{36} = 1

1 - \frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 0

4 x^{2} + y^{2} + 16 x + 16 y - 64 = 0

What is 36x^2+4y^2-49=0 ?
The solution to 36x^2+4y^2-49=0 is Ellipse with (h,k)=(0,0),a= 7/6 ,b= 7/2