Question 214701
Given the equation for an ellipse, find the length of the major axis:
{{{3x^2+4y^2 = 12}}} Re-arrange this to the standard form of the equation of an ellipse with major axis on the x-axis:{{{(x^2/a^2)+(y^2/b^2) = 1}}} where a = the semi-major axis and b = the semi-minor axis.
{{{3x^2+4y^2 = 12}}} Divide both sides by 12.
{{{(3x^2/12)+(4y^2/12) = 1}}} Simplify the left side.
{{{(x^2/4)+(y^2/3) = 1}}} Compare with the standard form:
{{{(x^2/a^2)+(y^2/b^2) = 1}}}
{{{a^2 = 4}}} Take the square root of both sides.
{{{a = 2}}} This is the length of the semi-major axis.
{{{2a = 4}}} This is the length of the major axis.