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What is an equation in standard form of an ellipse centered at the origin with vertex (-6,0) and co-vertex (0,4)?

2 Answers

5 votes

(x^(2) )/(36) +
( y^(2))/(16) = 1

This is because the standard form of an ellipse is


( x^(2) )/( a^(2) ) +
( y^(2) )/( b^(2) ) = 1

where a is the vertex and b is the co-vertex. So when we stick their respective x and y values in and then square them, you're left with the answer above.
User Shivachandra
by
8.2k points
6 votes

Answer:


(x^(2) )/(36)+(y^(2) )/(16)=1

Explanation:

As we know standard equation of n ellipse is
((x-0)^(2) )/((-6)^(2))+((y-0)^(2) )/((4)^(2) )=1

In the given equation (h, k) is the center, a is the vertex and b is the co-vertex.

Here vertex is (-6, 0) and co-vertex is (0, 4)

Therefore, length of a = -6, b = 4 and origin is (0, 0)

Now the equation of the ellipse will be


((x-0)^(2) )/((-6)^(2))+((y-0)^(2) )/((4)^(2) )=1


(x^(2) )/(6^(2))+(y^(2) )/(4^(2) )=1


(x^(2) )/(36)+(y^(2) )/(16)=1

Therefore, the equation of the ellipse will be
(x^(2) )/(36)+(y^(2) )/(16)=1

What is an equation in standard form of an ellipse centered at the origin with vertex-example-1
User Kalam
by
9.9k points

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