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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
Solution
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
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