What is 7x^2+18y^2=63 ?

The solution to 7x^2+18y^2=63 is Ellipse with (h,k)=(0,0),a=3,b=sqrt(7/2)

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7x^2+18y^2=63

7 x^{2} + 18 y^{2} = 63

(h, k) = (0, 0), a = 3, b = \frac{7}{2}

Solution steps

7 x^{2} + 18 y^{2} = 63

Rewrite

7 x^{2} + 18 y^{2} = 63

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{7}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = \frac{7}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 3, b = \frac{7}{2}

\frac{( x + 3 ) ^{2}}{100} + \frac{( y + 4 ) ^{2}}{32} = 1

\frac{x ^{2}}{7} + \frac{y ^{2}}{4} = 1

\frac{( x - 2 ) ^{2}}{5} + \frac{( y + 3 ) ^{2}}{9} = 1

4 x^{2} + 9 y^{2} - 24 x + 18 y + 9 = 0

16 x^{2} + 9 y^{2} - 64 x + 54 y + 1 = 0

What is 7x^2+18y^2=63 ?
The solution to 7x^2+18y^2=63 is Ellipse with (h,k)=(0,0),a=3,b=sqrt(7/2)