Question

Answer the following :

Find the equations of the tangents to the circle x² + y² = 16 with slope –2

Answer 1

The equations of the tangents to the circle x² + y² = a² in terms of slope m are

y = `"m"x ± "a"sqrt(1 + "m"^2)`

The radius of the given circle is a = 4 and slope of the tangent is m = – 2.

∴ `"a"sqrt(1 + "m"^2) = 4sqrt(1 + (-2)^2) = 4sqrt(5)`

∴ the equations of required tangents are

y = `-2x ± 4sqrt(5)`

i.e., `2x + y ± 4sqrt(5)` = 0