Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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The Radius of the Circle Represented by the Equation 3x2 + 3y2 + λXy + 9x + (λ − 6) Y + 3 = 0 is - Mathematics

MCQ

The radius of the circle represented by the equation 3x2 + 3y2 + λxy + 9x + (λ − 6) y + 3 = 0 is

Options

  • \[\frac{3}{2}\]

  • \[\frac{\sqrt{17}}{2}\]

  •  2/3

  • none of these

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Solution

\[\frac{3}{2}\]

The equation of the circle is 3x2 + 3y2 + λxy + 9x + (λ − 6) y + 3 = 0.
∴ Coefficient of xy = 0

\[\Rightarrow \lambda = 0\]

\[\therefore 3 x^2 + 3 y^2 + 9x - 6y + 3 = 0\]

\[ \Rightarrow x^2 + y^2 + 3x - 2y + 1 = 0\]

Therefore, the radius of the circle is

\[\sqrt{\left( \frac{3}{2} \right)^2 + \left( - 1 \right)^2 - 1} = \frac{3}{2}\] .
Concept: Circle - Standard Equation of a Circle
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Q 5 | Page 39
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