Write the equation of the ellipse with center at $( 5,1 ) , a = 5 , b = 2$ and major axis parallel to the x-axis.
A) $\quad \frac { ( x - 5 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$
B) $\quad \frac { ( x - 5 ) ^ { 2 } } { 4 } + \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$
C) $\quad \frac { ( x - 5 ) ^ { 2 } } { 25 } - \frac { ( y - 1 ) ^ { 2 } } { 4 } = 1$
D)
$$\frac { ( x - 5 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 4 } = - 1$$

Question

Quizplus · Accepted Answer

The equation of an ellipse with its center at $(h, k)$, major axis length $2a$, minor axis length $2b$, and major axis parallel to the x-axis is $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$. Given $h=5$, $k=1$, $a=5$, and $b=2$, substituting these values gives $\frac{(x-5)^2}{25} + \frac{(y-1)^2}{4} = 1$, which matches choice A.

Write the Equation of the Ellipse with Center At (5,1),a=5,b=2( 5,1 ) , a = 5 , b = 2(5,1),a=5,b=2

Write the Equation of the Ellipse with Center At $( 5,1 ) , a = 5 , b = 2$