What is 5x^2+7y^2=70 ?

The solution to 5x^2+7y^2=70 is Ellipse with (h,k)=(0,0),a=sqrt(14),b=sqrt(10)

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5x^2+7y^2=70

5 x^{2} + 7 y^{2} = 70

(h, k) = (0, 0), a = 14, b = 10

Solution steps

5 x^{2} + 7 y^{2} = 70

Rewrite

5 x^{2} + 7 y^{2} = 70

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 14 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 10 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 14, b = 10

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 14, b = 10

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

9 x^{2} + 25 y^{2} - 18 x - 250 y + 409 = 0

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

a - bi = \frac{1}{a + bi}

x^{2} + 4 y^{2} + 20 x + 44 y + 121 = 0

What is 5x^2+7y^2=70 ?
The solution to 5x^2+7y^2=70 is Ellipse with (h,k)=(0,0),a=sqrt(14),b=sqrt(10)