Question

question 15 of 20 which conic section does the equation below describe? (x - 3)^2 / 40+(y + 5)^2 / 4 = 1 a. parabola b. circle c. ellipse d. hyperbola

Explanation:

Step1: Recall conic - section equations

The general form of an ellipse centered at \((h,k)\) is \(\frac{(x - h)^2}{a^2}+\frac{(y - k)^2}{b^2}=1\) (\(a
eq b\)), for a circle \(\frac{(x - h)^2}{a^2}+\frac{(y - k)^2}{a^2}=1\), for a parabola it is of the form \(y=ax^{2}+bx + c\) or \(x = ay^{2}+by + c\), and for a hyperbola \(\frac{(x - h)^2}{a^2}-\frac{(y - k)^2}{b^2}=1\) or \(\frac{(y - k)^2}{a^2}-\frac{(x - h)^2}{b^2}=1\).

Step2: Analyze the given equation

The given equation \(\frac{(x - 3)^2}{40}+\frac{(y + 5)^2}{4}=1\) is in the form \(\frac{(x - h)^2}{a^2}+\frac{(y - k)^2}{b^2}=1\) where \(h = 3\), \(k=-5\), \(a^{2}=40\), \(b^{2}=4\) and \(a
eq b\).

Answer:

C. Ellipse