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What type of conic is given by the equation 4x^2+9y^2=36

User Dayong
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1 Answer

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Answer:

This is equation of ellipse

Explanation:

we are given


4x^2+9y^2=36

We can see that right side is 36

so, we can make right side as 1 by dividing both sides by 36


(4x^2+9y^2)/(36) =(36)/(36)


(4x^2+9y^2)/(36) =1


(4x^2)/(36)+(9y^2)/(36) =1

we can simplify it


(x^2)/(9)+(y^2)/(4) =1

we can rewrite it as


(x^2)/(3^2)+(y^2)/(2^2) =1

now, we can compare it with standard equation of ellipse


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

we can see that both equations are similar

so, this is equation of ellipse

User Doppelganger
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