Question

An ellipse has a vertex at (0, −7), a co-vertex at (4, 0), and a center at the origin. Which is the equation of the ellipse in standard form?

Answer 1

As Per Provided Information

An ellipse has a vertex at (0, −7), a co-vertex at (4, 0), and a center at the origin (0,0) .

We have been asked to find the equation of the ellipse in standard form .

As we know the standard equation of an ellipse with centre at the origin (0,0). Since its vertex is on y-axis

`\underline\purple{\boxed{\bf \: \frac{ {y}^(2) }{ {a}^(2) } \: + \: \frac{ {x}^(2) }{ {b}^(2) } = \: 1}}`

where,

• a = -7
• b = 4

Substituting these values in the above equation and let's solve it

`\qquad\sf \longrightarrow \: \frac{ {y}^(2) }{ {( - 7)}^(2) } \: + \frac{ {x}^(2) }{ {(4)}^(2) } = 1 \\ \\ \\ \qquad\sf \longrightarrow \: \frac{ {y}^(2) }{49} \: + \frac{ {x}^(2) }{16} = 1 \\ \\ \\ \qquad\sf \longrightarrow \: \: \frac{ {x}^(2) }{16} \: + \frac{ {y}^(2) }{49} = 1`

Therefore,

• Required standard equation is x²/16 + y²/16 = 1

So, your answer is 2nd Picture.