How do you write an equation of an ellipse in standard form with centre at (-2,8) and a major axis (parallel to the x-axis) length of 12 units and a minor axis of 10 units?

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How do you write an equation of an ellipse in standard form with centre at (-2,8) and a major axis (parallel to the x-axis) length of 12 units and a minor axis of 10 units?

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Answer 1 · 2016-09-13T01:41:42

We know that the standard equation of an ellipse having coordinate of its center $(α, β)$ $(alpha,beta)$ , major axis parallel to x-axis and length of the semi-major axis and semi-minor axis as $a and b$ $a and b$ respectively ,is

$\frac{{(x - α)}^{2}}{a^{2}} + \frac{{(y - β)}^{2}}{b^{2}} = 1$ $(x-alpha)^2/a^2+(y-beta)^2/b^2=1$

Inserting

$α = - 2 and β = 8$ $alpha=-2 and beta =8$

$a = \frac{12}{2} = 6 and b = \frac{10}{2} = 5$ $a=12/2=6 and b=10/2=5$

we get the standard equation of the ellipse

$\frac{{(x + 2)}^{2}}{6^{2}} + \frac{{(y - 8)}^{2}}{5^{2}} = 1$ $(x+2)^2/6^2+(y-8)^2/5^2=1$

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How do you write an equation of an ellipse in standard form with centre at (-2,8) and a major axis (parallel to the x-axis) length of 12 units and a minor axis of 10 units?

1 Answer

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