Question

Choose the correct conic section to fit the equation. 49x 2 - 16y 2 = 784 Circle Ellipse Parabola Hyperbola

Answer 1

Thus, The conic which fits the given equation correctly is hyperbola

Explanation:

The equation is given to be : 49x² - 16y² = 784

Now, we need to find the correct conic section which fits this given equation

So, to find the correct conic, we will reduce the given equation into the standard form :

So, make R.H.S. 1 by dividing each term by 784

`(49x^2)/(784)-(16y^2)/(784)=(784)/(784)`

`\implies (x^2)/(16)-(y^2)/(49)=1`

`\implies(x^2)/(4^2)-(y^2)/(7^2)=1`

This is the standard equation of hyperbola, where a = 4 and b = 7

Thus, The conic which fits the given equation correctly is hyperbola

Answer 2

hyperbola

Explanation:

49x^ 2 - 16y^ 2 = 784

Divide each side by 784

49/784x^ 2 - 16/784y^ 2 = 784

x^2/16 - y^2/49 = 1

This is a hyperbola centered at (0,0)

If it has subtraction, it has to be a hyperbola