Maharashtra State BoardHSC Science (Electronics) 11th
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Answer the following : Find the equations of the tangents to the circle x2 + y2 = 36 which are perpendicular to the line 5x + y = 2 - Mathematics and Statistics

Sum

Answer the following :

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

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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 = awith 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

Concept: Tangent
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 6 Circle
Miscellaneous Exercise 6 | Q II. (23) | Page 138
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