What are the intercepts of 9x2 plus 4y equals 36?

Answer 1

9x2 + 4y = 36
∴ 4y = 36 - 9x2
∴ y = 9 - 9x2/4

also:

∴ 9x2 = 36 - 4y
∴ x2 = 4 - 4y/9
∴ x = (4 - 4y/9)1/2

This equation represents a parabolic curve, so we know it will intercept the y-axis at one point, and the x-axis at either zero or two points. Let's start with the x-axis:

y = 9 - 9x2/4

Let y = 0:
∴ 0 = 9 - 9x2/4
∴ 0 = 36 - 9x2
∴ 9x2 = 36
∴ x2 = 4
∴ x = +/- 2

So the curve intercepts the x axis at the points -2, 0 and 2, 0

As for the y axis:
x = (4 - 4y/9)1/2
Let x = 0:
∴ 0 = (4 - 4y/9)1/2
∴ 0 = 4 - 4y/9
∴ 0 = 45 - 4y
∴ 4y = 45
∴ y = 45/4 = 11 1/4
So the curve intercepts the y axis at the point 0, 11.25