Question

Nrite an equation of the ellipse with foci at (3, 0) and co-vertices at (0, +_1).

Answer 1

Answer:

$\frac{ {x}^{2} }{10} + {y}^{2} = 1$

Step-by-step explanation:

Equation of ellipse is

$\frac{(x - h) {}^{2} }{ {a}^{2} } + \frac{(y - k) {}^{2} }{ {b}^{2} } = 1$

Where h,k is center

A is the length of semi-major axis. This axis include the foci

b is length of semi-minor axis. This axis includes main vertices.

Since we have 0,1 and 0,-1 as co-vertices, the length of the minor axis is 2 so the length of the semi-major is 1.

So we have now,

$\frac{(x - h) {}^{2} }{ {a}^{2} } + \frac{(y - k) {}^{2} }{1} = 1$

Next, to since the foci has a y coordinate of 0 and the co-vertrx has a x coordinate of 0, our center is 0,0

so we have

$\frac{ {x}^{2} }{ {a}^{2} } + {y}^{2} = 1$

Now, we can do equation

${a}^{2} - {b}^{2} = {c}^{2}$

B^2=1

C^2 is 9

${a}^{2} - 1 = 9$

${a}^{2} = 10$

S0, we now have

$\frac{ {x}^{2} }{10} - {y}^{2} = 1$