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anzhelika [568]
3 years ago
6

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

Mathematics
1 answer:
zvonat [6]3 years ago
8 0

Answer:

This is equation of ellipse

Step-by-step 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

\frac{4x^2+9y^2}{36} =\frac{36}{36}

\frac{4x^2+9y^2}{36} =1

\frac{4x^2}{36}+\frac{9y^2}{36} =1

we can simplify it

\frac{x^2}{9}+\frac{y^2}{4} =1

we can rewrite it as

\frac{x^2}{3^2}+\frac{y^2}{2^2} =1

now, we can compare it with standard equation of ellipse

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

we can see that both equations are similar

so, this is equation of ellipse

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