The foci are located as points A and B on the graph of the ellipse.
What is an ellipse?
Given 9x² + 16y² = 144.
This represents an ellipse equation.
To sketch the graph, we first rewrite the equation in standard form:
x²/(4/3)² + y²/3²= 1
This gives the semi-major axis a = 3 and the semi-minor axis b = 4/3.
The foci F of an ellipse are given by
c = √a² - b²
c = √3² - (4/3)²
c = √9 - 16/9
c =√65/9
c = √7.222
c = +-2.7
The foci will be on the major axis, so they will be along the x-axis.
The foci are located as points A and B on the graph of the ellipse.