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Chapter 6: Problem 4

Match the conic with its eccentricity. (a) \(01\) (i) parabola (ii) hyperbola (iii) ellipse

Short Answer

Expert verified
(a) matches with (iii) ellipse, (b) matches with (i) parabola, and (c) matches with (ii) hyperbola.

Step by step solution

01

Match the Curve with Eccentricity \(0

The given eccentricity is \(0<e<1\). This indicates the shape of a conic section: if the eccentricity is less than 1, it forms an ellipse. So, the match for (a) is (iii) ellipse.
02

Match the Curve with Eccentricity \(e=1\)

The given eccentricity is \(e=1\). A conic section with an eccentricity equal to 1 forms a parabola. So, the match for (b) is (i) parabola.
03

Match the Curve with Eccentricity \(e>1\)

The given eccentricity is \(e>1\). This indicates the conic section represents a hyperbola. So, the match for (c) is (ii) hyperbola.

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