The foci of the conic 25 x^2+16 y^2-150 x=175 are

Step-by-step solution

Transform the equation to standard ellipse form: Starting with 25x^2 + 16y^2 - 150x = 175 , complete the square in x : 25(x^2 - 6x) + 16y^2 = 175 25(x - 3)^2 + 16y^2 = 400 Divide by 400 to obtain standard ellipse form: (x-3)^2 16 + y^2 25 = 1 Identify ellipse parameters: The center is at (3, 0) . Since 25 > 16 , the semi-major axis a = 5 and semi-minor axis b = 4 along the y and x directions respectively. The focal distance is c = a^2 - b^2 = 25 - 16 = 3 . Locate the foci: With major axis vertical, the foci are loc