Final answer:
To find the equation of the straight line joining the foci of the given ellipses, we first need to determine the coordinates of the foci for each ellipse. Once we have the coordinates, we can use the point-slope form of a line to find the equation of the line. The equation of the line will be in the form y = mx + b, where m is the slope and b is the y-intercept.
Step-by-step explanation:
To find the equation of the straight line joining the two foci of the given ellipses, we need to find the coordinates of the foci first. The equation of an ellipse in standard form is (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h,k) represents the center, and 'a' and 'b' represent the lengths of the major and minor axes, respectively. Comparing the given equations with the standard form, we can determine the values of 'a' and 'b' for each ellipse.
Once we have the coordinates of the foci for both ellipses, we can use the point-slope form of a line to find the equation of the line joining the foci. The formula for the point-slope form is y = mx + b, where 'm' is the slope and 'b' is the y-intercept. By finding the slope and one point on the line (one of the foci), we can substitute these values into the point-slope form to obtain the equation of the line.
Therefore, the equation of the straight line joining the foci of the given ellipses is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.