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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?

An Ellipse Has A Vertex At 0 7 A Covertex At 4 0 And A Center At The Origin Which Is The Equation Of The Ellipse In Standard Form class=
An Ellipse Has A Vertex At 0 7 A Covertex At 4 0 And A Center At The Origin Which Is The Equation Of The Ellipse In Standard Form class=
An Ellipse Has A Vertex At 0 7 A Covertex At 4 0 And A Center At The Origin Which Is The Equation Of The Ellipse In Standard Form class=
An Ellipse Has A Vertex At 0 7 A Covertex At 4 0 And A Center At The Origin Which Is The Equation Of The Ellipse In Standard Form class=

Sagot :

Answer:

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

[tex] \underline\purple{\boxed{\bf \: \dfrac{ {y}^{2} }{ {a}^{2} } \: + \: \dfrac{ {x}^{2} }{ {b}^{2} } = \: 1}}[/tex]

where,

  • a = -7
  • b = 4

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

[tex] \qquad\sf \longrightarrow \: \dfrac{ {y}^{2} }{ {( - 7)}^{2} } \: + \dfrac{ {x}^{2} }{ {(4)}^{2} } = 1 \\ \\ \\ \qquad\sf \longrightarrow \: \dfrac{ {y}^{2} }{49} \: + \frac{ {x}^{2} }{16} = 1 \\ \\ \\ \qquad\sf \longrightarrow \: \: \dfrac{ {x}^{2} }{16} \: + \dfrac{ {y}^{2} }{49} = 1[/tex]

Therefore,

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

So, your answer is 2nd Picture.

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