   Chapter 10.1, Problem 24E

Chapter
Section
Textbook Problem

# Sketching an Ellipse In Exercises 25–30, find the center, foci, vertices, and eccentricity of the ellipse, and sketch its graph. 3 x 2 + 7 y 2 = 63

To determine
The centre, vertex, foci and eccentricity of the provided ellipse and sketch its graph.

Explanation

Given: 3x2+7y2=63

Explanation: Since the general form of ellipse is (xh)2a2+(yk)2b2=1 where a is the major axis and b is the minor axis with (h, k) as centre.

Divide both sides by 63 to make the R.H.S as 1 to get,

x221+y29= 1 where a is the major axis and b is the minor axis.

Since the provided ellipse has more value on a than b. So the major axis in this case is the x axis, that means it’s an ellipse of the first type

So here a2=21 and b2=9

T

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