What is 7x^2+16y^2=112 ?

The solution to 7x^2+16y^2=112 is Ellipse with (h,k)=(0,0),a=4,b=sqrt(7)

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7x^2+16y^2=112

7 x^{2} + 16 y^{2} = 112

(h, k) = (0, 0), a = 4, b = 7

Solution steps

7 x^{2} + 16 y^{2} = 112

Rewrite

7 x^{2} + 16 y^{2} = 112

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{( 7 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 7

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 4, b = 7

2 x^{2} + 10 y^{2} + 10 x - 6 y - 10 = 0

x^{2} + y^{2} - 4 y \leq 0

\frac{x ^{2}}{16} + \frac{( y + 4 ) ^{2}}{81} = 1

16 - 4 x^{2} - y^{2} \geq 0

\frac{x ^{2}}{49} + \frac{y ^{2}}{4} = 1

What is 7x^2+16y^2=112 ?
The solution to 7x^2+16y^2=112 is Ellipse with (h,k)=(0,0),a=4,b=sqrt(7)