Graph the Ellipse 36x^2+y^2-36=0

Question

36x^2+y^2-36=0 , please help! I re-read the instructions and steps so many times and still just don't get it

Answer 1

Given equation 36x^2+y^2-36 = 0

Add 36 to each side.

36x^2+y^2-36+36 = 0+36

36x^2+y^2 = 36

Divide to each side by 36.

36x^2/36+y^2/36 = 36/36

x^2/1+y^2/36 = 1

Ellipse equation is (x-h)^2/a^2+(y-k)^2/b^2 = 1

Here centre (h,k) = (0,0)

Compare it to standerd form of ellipse equation x^2/b^2+y^2/a^2 = 1

When a > b and it is passes through origin.

Graph of given ellipse.

 

Answer 2

The equation is

The standard form for an ellipse is in a form = 1, So divide both sides of equation by 36 to set it equal to 1.

Compare the standardform of ellipse

a ² > b ²

If the larger denominator is under the "y " term, then the ellipse is vertical.Center (h, k ).

a  = length of semi-major axis, b  = length of semi-minor axis.

(h, k ) = (0, 0)

a = 6 , b = 1

The points for this ellipse are ,

Right most point (h +b , k )

Left most point (h - b , k )

Top most point (h , k + a )

Bottom most point (h , k - a )

Right most point (1, 0)

Left most point (-1, 0)

Top most point (0, 6)

Bottom most point (0, -6)

Graph

1. draw the coordinate plane.

2. Plot the center at (0, 0).

3.Plot 4 points away from the center in the up, down, left and right direction.

4.Sketch the ellipse.