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The differential equation of all straight lines touching the circle x^2+y^2=a^2 is

The differential equation of all straight lines touching the circle x^2+y^2=a^2 is
 

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Grade:12

1 Answers

Samyak Jain
333 Points
5 years ago
Equation of tangent to the circle x2 + y2 = a2 in slope form is
y = mx \pm a\sqrt{1 + m^2}      ...(1)
Differentiate (1) with respect to x. \Rightarrow  dy/dx = m ,  \because a\sqrt{1 + m^2} is a constant, its differentiation is zero.
Put the value of m in (1).
So, y = (dy/dx)x \pm a\sqrt{1 + (dy/dx)^2}   \Rightarrow  y – x(dy/dx) = \pm a\sqrt{1 + (dy/dx)^2}
Squaring both sides we get,
(y – x dy/dx)2 = a2 (1 + (dy/dx)2).
Option (b) is correct.

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