What is y-3=-x/(4y)(x-12) ?

The solution to y-3=-x/(4y)(x-12) is Ellipse with (h,k)=(6, 3/2),a=3sqrt(5),b=(3sqrt(5))/2

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y-3=-x/(4y)(x-12)

y - 3 = - \frac{x}{4 y} (x - 12)

(h, k) = (6, \frac{3}{2}), a = 35, b = \frac{3 5}{2}

Solution steps

y - 3 = - \frac{x}{4 y} (x - 12)

Rewrite

y - 3 + \frac{x}{4 y} (x - 12) = 0

in the form of the standard ellipse equation

\frac{( x - 6 ) ^{2}}{( 3 5 ) ^{2}} + \frac{( y - \frac{3}{2} ) ^{2}}{( \frac{3 5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (6, \frac{3}{2}), a = 35, b = \frac{3 5}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (6, \frac{3}{2}), a = 35, b = \frac{3 5}{2}

4 x^{2} - 34 y + 13 y^{2} - 36 = 0

5 x^{2} + 2 y^{2} + 12 y = - 8

\frac{( x + 7 ) ^{2}}{16} + \frac{( y + 5 ) ^{2}}{4} = 1

x^{2} + 3 \cdot y^{2} = 84

y^{2} = 9 - 4 x^{2}

What is y-3=-x/(4y)(x-12) ?
The solution to y-3=-x/(4y)(x-12) is Ellipse with (h,k)=(6, 3/2),a=3sqrt(5),b=(3sqrt(5))/2