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MathematicsCircleTangent & NormalEasy2 minPYQ_2020

MathematicsEasysingle choice

If the length of the chord of the circle, $x^{2} + y^{2} = r^{2} (r > 0)$ along the line, $y - 2 x = 3$ is $r$ , then $r^{2}$ is equal to:

Question diagram: If the length of the chord of the circle, x 2 + y 2 = r 2 (

Options:

Answer:

Solution:

$A B = r, A D = \frac{r}{2}$

$CD = rsin 60 ° = \frac{\sqrt{3} r}{2}$
$\Rightarrow \frac{|0 + 0 - 3|}{\sqrt{1^{2} + 2^{2}}} = \frac{\sqrt{3} r}{2} \Rightarrow r = 2 \sqrt{\frac{3}{5}} \Rightarrow r^{2} = \frac{12}{5}$

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Tangent & Normal

⏱ 2mℹ️ Source: PYQ_2020

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