What is 10x^2+7y^2-5=1 ?

The solution to 10x^2+7y^2-5=1 is Ellipse with (h,k)=(0,0),a=sqrt(3/5),b=sqrt(6/7)

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10x^2+7y^2-5=1

10 x^{2} + 7 y^{2} - 5 = 1

(h, k) = (0, 0), a = \frac{3}{5}, b = \frac{6}{7}

Solution steps

10 x^{2} + 7 y^{2} - 5 = 1

Rewrite

10 x^{2} + 7 y^{2} - 5 = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{3}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{6}{7} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{3}{5}, b = \frac{6}{7}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{6}{7}, a = \frac{3}{5}

0.11 x^{2} + 0.25 y^{2} = 1

2 x^{2} + 3 y^{2} + 4 x = 1

3 x^{2} + 8 y^{2} + 12 x + 48 y + 60 = 0

16 x^{2} + 25 y^{2} + 32 x - 384 = 0

9 x^{2} + 4 y^{2} - 36 x + 24 y - 1 = 0

What is 10x^2+7y^2-5=1 ?
The solution to 10x^2+7y^2-5=1 is Ellipse with (h,k)=(0,0),a=sqrt(3/5),b=sqrt(6/7)