Find the equation to the tangent to the circle x(squared)+y(squared)=5 which is perpendicular to the line 4x-2y+3=0.

slope of given line is 2, eqn is y = 2x + 3/2

its perpendicular eqn is of form , y = -1/2x + c where is c in intercept to be found ,as

this eqn is tangent , its perpendicular distance from center is equal to radius of 5 units

5 = c / (5/4)^1/2

so , c = 5/2*(5)^1/2

so eqn of tangent is : 2y + x - 5*(5)^1/2 =0

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regards

Ramesh