What is 16x^2+4y^2=49 ?

The solution to 16x^2+4y^2=49 is Ellipse with (h,k)=(0,0),a= 7/4 ,b= 7/2

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16x^2+4y^2=49

16 x^{2} + 4 y^{2} = 49

(h, k) = (0, 0), a = \frac{7}{4}, b = \frac{7}{2}

Solution steps

16 x^{2} + 4 y^{2} = 49

Rewrite

16 x^{2} + 4 y^{2} = 49

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{7}{4}, b = \frac{7}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{7}{2}, a = \frac{7}{4}

4 x^{2} + 8 y^{2} - 16 = 0

17 x^{2} + 10 y^{2} + 102 x + 80 y + 143 = 0

(6 p + 5 q) 2 = 36 p^{2} + 25 q^{2}

3 x^{2} + 54 x + 243 + 2 y^{2} - 6 = 0

4 x^{2} + 9 y^{2} - 24 x + 36 y - 72 = 0

What is 16x^2+4y^2=49 ?
The solution to 16x^2+4y^2=49 is Ellipse with (h,k)=(0,0),a= 7/4 ,b= 7/2