Question

Answer the following :

Find the equations of the tangents to the circle x² + y² = 4 which are parallel to 3x + 2y + 1 = 0

Answer 1

Given equation of the circle is

x² + y² = 4

Comparing this equation with x² + y² = a², we get

a² = 4

Given equation of the line is

3x + 2y + 1 = 0

Slope of this line = `(-3)/2`

Since, the required tangents are parallel to the given line.

∴ Slope of required tangents (m) =`(-3)/2`

Equations of the tangents to the circle x² + y² = a² with slope m are

y = `"m"x ± sqrt("a"^2 (1 + "m"^2)`

∴ the required equations of the tangents are

y = `(-3)/2x ± sqrt(4[1 + ((-3)/2)^2]`

= `(-3)/2x  ± sqrt(4(1 + 9/4)`

∴ y = `(-3)/2x  ± sqrt(13)`

∴ 2y = `3x ± 2sqrt(13)`

∴ `3x + 2y ± 2sqrt(13)` = 0