Question

Find the eccentricity of the conic represented by \( x^2 - y^2 - 4x + 4y + 16 = 0 \):

• A. 2
• B. \( \sqrt{2} \)
• C. \( 2\sqrt{2} \)
• D. \( \sqrt{3} \)

Hint:

For conics, the eccentricity can be found by converting the equation into standard form and applying the formula for eccentricity.

Answer 1

The Correct Option is B

Step 1: Rewrite the equation in standard form.
By completing the square and simplifying, we convert the given equation into the standard form of a hyperbola. The eccentricity \( e \) of a hyperbola is given by: \[ e = \sqrt{1 + \frac{b^2}{a^2}} \] Substituting the values, we find the eccentricity to be \( \sqrt{2} \).
Thus, the correct answer is (2).