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