If m i - 1- m i - i -1-2-3-4 are con - cyclic points- then the value of m 1 m 2 m 3 m 4 isA- -1B- 1C- 0D- None of these

The correct option is B 1 Let equation of circle be x^2 + y^2 + 2gx + 2fy + c = 0. If (m, 1/m) lies on this circle, then m^2 + 1/m^2 + 2gm + 2f1/m + c = 0 or m ...

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Byju's Answer

Standard IX

Mathematics

General Equation of Circle S=0

If m i , 1/ m...

Question

If $(m_{i}, \frac{1}{m_{i}})$ , i = 1, 2, 3, 4 are con - cyclic points, then the value of $m_{1} m_{2} m_{3} m_{4}$ is

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-1

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None of these

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Solution

The correct option is A
1

Let equation of circle be $x^{2} + y^{2}$ + 2gx + 2fy + c = 0. If $(m, \frac{1}{m})$ lies on this circle, then

$m^{2} + \frac{1}{m^{2}} + 2 g m + 2 f \frac{1}{m} + c = 0$

or $m^{4} + 2 g m^{3} + 2 f m + c m^{2} + 1 = 0$

This is a fourth degree equation in m having $m_{1}, m_{2}, m_{3}, m_{4}$ as its roots.

Therefore, $m_{1} m_{2} m_{3} m_{4}$ = product of roots = $\frac{1}{1}$ = 1.

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Similar questions

If $(m_{i}, \frac{1}{m_{i}})$ , i = 1, 2, 3, 4 are con - cyclic points, then the value of $m_{1}, m_{2}, m_{3}, m_{4}$ is

If $(m_{i}, \frac{1}{m_{i}})$ , i = 1, 2, 3, 4 are con - cyclic points, then the value of $m_{1} m_{2} m_{3} m_{4}$ is

Q. If

(m_{i}, \frac{1}{m_{i}}), i = 1, 2, 3, 4

are concyclic points then the value of

m_{1} m_{2} m_{3} m_{4}

is?

Q. If

(m_{i}, 1 / m_{i}), m_{i} > 0, i = 1, 2, 3, 4

are four distinct points on a circle , then show that

m_{1} m_{2} m_{3} m_{4} = 1

f (m_{i}, \frac{1}{m_{i}})

i = 1, 2, 3, 4

are four distinct points on the circle with centre origin, then value of

m_{1} m_{2} m_{3} m_{4}

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If (mi,1mi), i = 1, 2, 3, 4 are con - cyclic points, then the value of m1m2m3m4 is

The correct option is A 1 Let equation of circle be x2+y2 + 2gx + 2fy + c = 0. If (m,1m) lies on this circle, then m2+1m2+2gm+2f1m+c=0 or m4+2gm3+2fm+cm2+1=0 This is a fourth degree equation in m having m1,m2,m3,m4 as its roots. Therefore, m1m2m3m4 = product of roots = 11 = 1.

If $(m_{i}, \frac{1}{m_{i}})$ , i = 1, 2, 3, 4 are con - cyclic points, then the value of $m_{1} m_{2} m_{3} m_{4}$ is