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MathematicsCircleTangent & NormalMedium2 minPYQ_2019

MathematicsMediumsingle choice

The tangent and the normal lines at the point $(\sqrt{3}, 1)$ to the circle $x^{2} + y^{2} = 4$ and the $x$ -axis form a triangle. The area of this triangle (in square units) is:

Question diagram: The tangent and the normal lines at the point 3 , 1 to the c

Options:

Answer:

B

Solution:

Equation tangent at $P (\sqrt{3}, 1)$
$x \cdot \sqrt{3} + y \cdot 1 = 4$
x-intercept of this tangent is $\frac{4}{\sqrt{3}}$ .
Hence, area of $Δ = \frac{1}{2} \cdot \frac{4}{\sqrt{3}} \cdot 1 = \frac{2}{\sqrt{3}}$

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Tangent & Normal

⏱ 2mℹ️ Source: PYQ_2019

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