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Equation of Conics in Complex Form

Statement 1: ...

Question

Statement 1: Locus of z satisfying the equation $| z - 1 | + | z - 8 | = 5$ is an ellipse.
Statement 2: Sum of focal distances of any point on ellipse is constant.

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

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Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.

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Statement 1 is true and Statement 2 is false.

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Statement 1 is false and Statement 2 is true.

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Solution

The correct option is B Statement 1 is false and Statement 2 is true.
Statement 2 is true as it is the definition of an ellipse. Statement 1 is false as distance between 1 and 8 is 7 but $| z - 1 | + | z - 8 | = 5 < 7$ . Hence no such z exists.

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