Question

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

Answer 1

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