How do you write the equation of an ellipse with center at $(2, - 3)$ $(2,-3)$ the major axis is vertical and is 10 units long, and the minor axis is 4 units?

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Answer 1 · 2018-03-11T06:06:40

$\frac{{(x - 2)}^{2}}{4} + \frac{{(y + 3)}^{2}}{25} = 1$ $(x-2)^2/4 + (y+3)^2/25 = 1$

Given: vertical ellipse with center: $(2, - 3)$ $(2, -3)$ , major axis $= 10$ $= 10$ , minor axis $= 4$ $= 4$

vertical axis ellipse equation: $\frac{{(x - h)}^{2}}{b^{2}} + \frac{{(y - k)}^{2}}{a^{2}} = 1$ $(x-h)^2/b^2 + (y-k)^2/a^2 = 1$

$where center = (h, k); a = \frac{major axis}{2}; b = \frac{minor axis}{2}$ $" where center"= (h, k); a = ("major axis")/2; b = ("minor axis")/2$

$a = \frac{10}{2} = 5; a^{2} = 25$ $a = 10/2 = 5; " "a^2 = 25$ ; $b = \frac{4}{2} = 2; b^{2} = 4$ $" "b = 4/2 = 2; " "b^2 = 4$

$h = 2; k = - - 3 = + 3$ $h = 2; " " k = - -3 = +3$

vertical axis ellipse equation: $\frac{{(x - 2)}^{2}}{4} + \frac{{(y + 3)}^{2}}{25} = 1$ $(x-2)^2/4 + (y+3)^2/25 = 1$

How do you write the equation of an ellipse with center at (2,-3)(2,−3)(2,-3) the major axis is vertical and is 10 units long, and the minor axis is 4 units?