If m i - 1- m i - i -1-2-3-4 are four distinct points on a circle-then m 1 m 2 m 3 m 4-A- 4B- depends on radius onlyC- 1D- depends on radius and centre

The correct option is C 1Let the points ( m_i,1m_i ),i=1,2,3,4 lie on the circle x^2+y^2+2gx+2fy+c=0 ⇒m_i^2+1m_i^2+2gm_i+2fm_i+c=0, i=1,2,3,4 ⇒ m_i^4+ 2gm_i^3 ...

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Byju's Answer

Standard XII

Physics

1st Equation of Motion

if m i , 1/ m...

Question

if $(m_{i}, \frac{1}{m_{i}})$ , $i = 1, 2, 3, 4$ are four distinct points on a circle,
then $m_{1} m_{2} m_{3} m_{4} =$

1

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depends on radius only

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depends on radius and centre

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Solution

The correct option is A $1$
Let the points $(m_{i}, \frac{1}{m_{i}}), i = 1, 2, 3, 4$ lie on the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0 \Rightarrow m_{i}^{2} + \frac{1}{m_{i}^{2}} + 2 g m_{i} + \frac{2 f}{m_{i}} + c = 0, i = 1, 2, 3, 4 \Rightarrow m_{i}^{4} + 2 g m_{i}^{3} + c m_{i}^{2} + 1 = 0, i = 1, 2, 3, 4$
Now, $m_{1}, m_{2}, m_{3}, m_{4}$ are roots of the equation.
$∴ m_{1} \cdot m_{2} \cdot m_{3} \cdot m_{4} = 1$

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Similar questions

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if (mi,1mi), i=1,2,3,4 are four distinct points on a circle, then m1m2m3m4=

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if $(m_{i}, \frac{1}{m_{i}})$ , $i = 1, 2, 3, 4$ are four distinct points on a circle,
then $m_{1} m_{2} m_{3} m_{4} =$