If a circle passing through the point (-1, 0) touches y-axis at (0, 2), then the length of the chord of the circle along the x-axis is

Step-by-step Solution:

The equation of a circle is given by:

(x - h)² + (y - k)² = r²

where (h, k) is the center and r is the radius of the circle.

The circle passes through the point (-1, 0) and touches the y-axis at (0, 2).

Since the circle touches the y-axis, the distance from the center to the y-axis equals the radius of the circle. This gives the equation:

h² + k² = r²

From solving the system of equations, we find the center of the circle as (h, k) = (-1/2, 1) and the radius as r = √5 / 2.

The length of the chord of the circle along the x-axis is given by the formula:

L = 2 √(r² - k²)

Substituting the values of r = √5 / 2 and k = 1 into the formula:

L = 2 √((√5 / 2)² - 1²)

Calculating the chord length:

L = 2 √(5 / 4 - 1) = 2 √(1 / 4) = 2 × 1 / 2 = 1

The length of the chord of the circle along the x-axis is 1 unit.

Options:

• 3/2
• 5/2
• 3
• 5

Correct Option: 3