Question

The distance between the points \( (2\cos \theta, 0) \) and \( (0, 2\sin \theta) \) is:

• A. \( 1 \)
• B. \( 2 \)
• C. \( 3 \)
• D. \( 4 \)

Hint:

Use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Answer 1

The Correct Option is D

The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting \( (x_1, y_1) = (2\cos \theta, 0) \) and \( (x_2, y_2) = (0, 2\sin \theta) \):
\[ d = \sqrt{(0 - 2\cos \theta)^2 + (2\sin \theta - 0)^2} \] \[ = \sqrt{4\cos^2 \theta + 4\sin^2 \theta} \] \[ = \sqrt{4(\cos^2 \theta + \sin^2 \theta)} \] \[ = \sqrt{4 \times 1} = \sqrt{4} = 2 \]