What is 4x^2-16x+25y^2-84=0 ?

The solution to 4x^2-16x+25y^2-84=0 is Ellipse with (h,k)=(2,0),a=5,b=2

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4x^2-16x+25y^2-84=0

4 x^{2} - 16 x + 25 y^{2} - 84 = 0

(h, k) = (2, 0), a = 5, b = 2

Solution steps

4 x^{2} - 16 x + 25 y^{2} - 84 = 0

Rewrite

4 x^{2} - 16 x + 25 y^{2} - 84 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 0), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 0), a = 5, b = 2

16 (x - 4)^{2} + 25 (y + 2)^{2} = 400

8 x^{2} + 16 y^{2} = 1

\frac{( x - 8 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{1} = 1

4 x^{2} + 9 y^{2} \leq 36

x^{2} + 6 x + 9 + y^{2} = 28.09 + \frac{9 x ^{2}}{16}

What is 4x^2-16x+25y^2-84=0 ?
The solution to 4x^2-16x+25y^2-84=0 is Ellipse with (h,k)=(2,0),a=5,b=2