What is 53x^2+y^2=176 ?

The solution to 53x^2+y^2=176 is Ellipse with (h,k)=(0,0),a=(4sqrt(11))/(sqrt(53)),b=4sqrt(11)

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53x^2+y^2=176

53 x^{2} + y^{2} = 176

(h, k) = (0, 0), a = \frac{4 11}{53}, b = 411

Solution steps

53 x^{2} + y^{2} = 176

Rewrite

53 x^{2} + y^{2} = 176

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{4 11}{53} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 4 11 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{4 11}{53}, b = 411

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 411, a = \frac{4 11}{53}

2 x^{2} + 3 y^{2} + 8 x + 10 y - 2 = 0

2 x^{2} + 3 y^{2} - 8 x + 6 y - 7 = 0

530 x^{2} + 785 y^{2} + 1060 x - 1570 y = 24650

3 x^{2} + 2 y^{2} \leq 6

\frac{( x - 1 ) ^{2}}{36} + \frac{( y - 1 ) ^{2}}{25} = 1

What is 53x^2+y^2=176 ?
The solution to 53x^2+y^2=176 is Ellipse with (h,k)=(0,0),a=(4sqrt(11))/(sqrt(53)),b=4sqrt(11)