Question

Which of the following graphs represents quantity x minus 2 end quantity squared over 25 plus quantity y plus 4 end quantity squared over 7 equals 1 question mark (2 points) a ellipse with center at 2 comma negative 4 and points on ellipse at 2 comma 1, 2 comma negative 9, 2 plus square root 7 comma negative 4, and 2 minus square root 7 comma negative 4 b ellipse with center at 2 comma negative 4 and points on ellipse at seven comma negative 4, negative 3 comma negative 4, 2 comma negative 4 plus square root 7, and 2 comma negative 4 minus square root 7 c ellipse with center at negative 2 comma 4 and points on ellipse at negative 2 comma 9, negative 2 comma negative 1, negative 2 plus square root 7 comma 4, and negative 2 minus square root 7 comma 4 d ellipse with center at negative 2 comma 4 and points on ellipse at 3 comma 4, negative 7 comma 4, negative 2 comma 4 plus square root 7, and negative 2 comma 4 minus square root 7

Answer 1

The correct graph is Option B, representing an ellipse with center at (2, -4) and points that match the lengths of its semi-major and semi-minor axes, satisfying the equation (x - 2)^2 / 25 + (y + 4)^2 / 7 = 1.

The correct answer to the given question is option B.

The expression (x - 2)^2 / 25 + (y + 4)^2 / 7 = 1 represents the equation of an ellipse. To determine which graph represents this equation, we identify the center of the ellipse and its axes lengths.

The center of the ellipse is at (h, k) where h and k are derived from the form (x - h)^2 / a^2 + (y - k)^2 / b^2 = 1. Hence, the center is at (2, -4).

The length of the semi-major axis is √25 and the semi-minor axis is √7. Therefore, the ellipse will have points at (2, -4 + √7) and (2, -4 - √7) along the y-axis, and (2 + √25, -4) and (2 - √25, -4) along the x-axis.

Option B is the correct graph since it matches the description with its center at (2, -4) and has points on the ellipse at (2, -4 + √7), (2, -4 - √7), (2 + √25, -4), and (2 - √25, -4).