Match each graph to equations A-H. A. ((x-2)^2)/(4)+((y-1)^2)/(9)=1 B. ((x-2)^2)/(4)+((y-1)^2)/(

step 1 In this question, we are going to match the graph of the ellipse that's given to the correct equ

Match each graph to equations A-H. A....

Match each graph to equations $\mathrm{A}-\mathrm{H}$. A. $\frac{(x-2)^{2}}{4}+\frac{(y-1)^{2}}{9}=1$ B. $\frac{(x-2)^{2}}{4}+\frac{(y-1)^{2}}{16}=1$ C. $\frac{(x-2)^{2}}{16}+\frac{(y-1)^{2}}{4}=1$ D. $\frac{(x-2)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$ E. $\frac{(x+2)^{2}}{4}+\frac{(y+1)^{2}}{9}=1$ F. $\frac{(x+2)^{2}}{4}+\frac{(y+1)^{2}}{16}=1$ G. $\frac{(x+2)^{2}}{16}+\frac{(y+1)^{2}}{4}=1$ H. $\frac{(x+2)^{2}}{9}+\frac{(y+1)^{2}}{4}=1$

Match each graph to equations $\mathrm{A}-\mathrm{H}$.
A. $\frac{(x-2)^{2}}{4}+\frac{(y-1)^{2}}{9}=1$
B. $\frac{(x-2)^{2}}{4}+\frac{(y-1)^{2}}{16}=1$
C. $\frac{(x-2)^{2}}{16}+\frac{(y-1)^{2}}{4}=1$
D. $\frac{(x-2)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$
E. $\frac{(x+2)^{2}}{4}+\frac{(y+1)^{2}}{9}=1$
F. $\frac{(x+2)^{2}}{4}+\frac{(y+1)^{2}}{16}=1$
G. $\frac{(x+2)^{2}}{16}+\frac{(y+1)^{2}}{4}=1$
H. $\frac{(x+2)^{2}}{9}+\frac{(y+1)^{2}}{4}=1$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Graphical Transformation of Conic Sections

Changing the values of h and k in the ellipse equation translates the graph horizontally and vertically, while altering a and b changes the size and shape of the ellipse. Recognizing these parameters allows one to match equations to their corresponding graphs by comparing centers, axis lengths, and overall orientation.

Center and Axes Identification

The terms (x-h) and (y-k) in the ellipse equation indicate a translation of the ellipse's center from the origin to the point (h, k). The denominators, a² and b², determine the lengths of the semi-major and semi-minor axes; the larger denominator corresponds to the longer axis of the ellipse, which aids in graphing the ellipse accurately.

Standard Form of an Ellipse

An ellipse in the plane is typically represented by its standard form equation, (x-h)²/a² + (y-k)²/b² = 1, where (h, k) is the center of the ellipse and a and b represent the semi-axis lengths along the x and y directions respectively. This form helps in quickly identifying the key characteristics and orientation of the ellipse.

Transcript

Please give Ace some feedback