I do not know how to change this equation: 16= 16x^2+y^2 into a standard ellipse equation
The standard equation of an ellipse is (x^2/b^2) + (y^2/a^2) = 1
In order to change the equation given into this form, we have to make the equation equal to 1 by dividing both sides of the equation by 16.
1) 16/16 = 16x^2/16 + y^2/16
The left side of the equation, 16/16, simplifies to be 1
The right side of the equation, 16x^2/16 + y^2/16, simplifies to be x^2/1 + y^2/16
2) 1 = x^2/1 + y^2/16
Now, the standard equation of an ellipse says (x^2/b^2) + (y^2/a^2) = 1
In the standard equation of an ellipse, the denominator of x^2 is b^2
In our equation, x^2/1 + y^2/16 = 1, the denominator of x^2 is 1.
Therefore, b^2 = 1
If we square root both sides, we find that b = 1
If we substitute 1 for b, in the equation, x^2/b^2 + y^2 = 1, we get x^2/1^2 + y^2/16 = 1
In the standard equation of an ellipse, x^2/b^2 + y^2/a^2 = 1, the denominator of y^2 is a^2
In our equation, x^2/1 + y^2/16 = 1, the denominator of y^2 is 16
Therefore, a^2 = 16
If we square root both sides, a = 4
If we substitute 4 for a in the equation, x^2/b^2 + y^2/a^2 = 1, we get x^2/1^2 + y^2/4^2 = 1, which is the final answer.
Hope this helped! Please let me know if you have any other questions! :)