Question

Answer the following :

Find the equations of the tangents to the circle x² + y² = 36 which are perpendicular to the line 5x + y = 2

Answer 1

Given equation of the circle is

x² + y² = 36

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

a² = 36

Given equation of line is 5x + y = 2

Slope of this line = – 5

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

∴ Slope of required tangents (m) = `1/5`

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 = `1/5x ± sqrt(36[1 + (1/5)^2]`

= `1/5x ± sqrt(36(1 + 1/25)`

∴ y = `1/5x ± 6/5 sqrt(26)`

∴ 5y = `x ± 6sqrt(26)`

∴ `x - 5y ± 6sqrt(26)` = 0