Question

Write in Standard Form 9x²+4y²=36

a) x²/4+x²/9=1
b) x²/9+x²/4=1
c) x²/36+x²/9=1
d) x²/9+x²/36=1

Answer 1

The standard form of the equation 9x²+4y²=36 is x²/4 + y²/9 = 1, after dividing each term by the constant 36.

Step-by-step explanation:

To write the equation 9x²+4y²=36 in standard form, we need to divide each term by the constant on the right side of the equation, which is 36, to achieve the equation of an ellipse in the standard form. Doing so yields the equation x²/4 + y²/9 = 1. This is now in the standard form of an ellipse where the coefficients of x² and y² are the reciprocals of the squares of the ellipse's semi-axes lengths. Moreover, to correct a typo from the options provided in the question, the answer should be x²/4 + y²/9 = 1, which matches option a from the choices given.