What is 4x^2-16x+3y^2+24y+52=0 ?

The solution to 4x^2-16x+3y^2+24y+52=0 is Ellipse with (h,k)=(2,-4),a=sqrt(3),b=2

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4x^2-16x+3y^2+24y+52=0

4 x^{2} - 16 x + 3 y^{2} + 24 y + 52 = 0

(h, k) = (2, - 4), a = 3, b = 2

Solution steps

4 x^{2} - 16 x + 3 y^{2} + 24 y + 52 = 0

Rewrite

4 x^{2} - 16 x + 3 y^{2} + 24 y + 52 = 0

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( 3 ) ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, - 4), a = 3, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 4), b = 2, a = 3

x = 1 - y^{2}

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

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

9 x^{2} - 4 y^{2} - 90 x - 32 y = - 305

f (x) = x^{2} - 6 x + 2

What is 4x^2-16x+3y^2+24y+52=0 ?
The solution to 4x^2-16x+3y^2+24y+52=0 is Ellipse with (h,k)=(2,-4),a=sqrt(3),b=2