What is 144=4x^2+y^2 ?

The solution to 144=4x^2+y^2 is Ellipse with (h,k)=(0,0),a=6,b=12

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144=4x^2+y^2

144 = 4 x^{2} + y^{2}

(h, k) = (0, 0), a = 6, b = 12

Solution steps

144 = 4 x^{2} + y^{2}

Rewrite

144 = 4 x^{2} + y^{2}

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 6, b = 12

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 12, a = 6

9 x^{2} + 18 x + 16 y^{2} - 64 y - 71 = 0

16 x^{2} + 36 y^{2} - 96 x + 144 y + 144 = 0

9 x^{2} + 36 x + 16 y^{2} - 96 y = - 36

4 - 12 x^{2} - 36 y^{2} \geq 0

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

What is 144=4x^2+y^2 ?
The solution to 144=4x^2+y^2 is Ellipse with (h,k)=(0,0),a=6,b=12