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Slope Form of Tangent

Find the equa...

Question

Find the equation of the tangents to the circle $x^{2} + y^{2} = 9$ which make an angle of $60^{\circ}$ with the x-axis.

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Solution

$E q u a t i o n o f t a n g e n t : y = m x + a \sqrt{m^{2} + 1} . \Rightarrow y = m x + 3 \sqrt{m^{2} + 1} . m = t a n 60 = \sqrt{3} . \Rightarrow y = \sqrt{3} x + 3 \sqrt{3 + 1} \Rightarrow y = \sqrt{3} x + 3 \times 2 \Rightarrow y = \sqrt{3 x} + 6.$

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