Question

Choose the correct alternative:

The equation of the tangent to the circle x² + y² = 4 which are parallel to x + 2y + 3 = 0 are

Options

• x − 2y = 2

• x + 2y = `± 2sqrt(3)`

• x + 2y = `± 2sqrt(5)`

• x − 2y = `± 2sqrt(5)`

Answer 1

x + 2y = `± 2sqrt(5)`

Explanation:

y = `"mx" ± "a" sqrt(1 + "m"^2)`

a = radius = 2

Slope of required line = `-1/2`

y = `-1/2"x" ± 2sqrt(1 + 1/4)`

y = `-"x"/2 ± 2sqrt5/2`

2y = `− "x" ± 2sqrt5`

∴ x + 2y = `±2sqrt5`