Let A Circle Be Given By 2x(x – a) + y(2y – b) = 0, (a ≠ 0, b ≠ 0). Find The Condition On A And B, If Two Chords Each Bisected By The x – Axis Can Be Drawn To The Circle From 

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Question

Let a circle be given by 2x(x – a) + y(2y – b) = 0, (a  0, b ≠ 0). Find the condition on a and b, if two chords each bisected by the x – axis can be drawn to the circle from 

Solution

Correct option is

a2 > 2b2.

Equation of the given circle is 

                  2x (x – a) + y (2y – b) = 0   

          or      2x2 – 2ax + 2y2 – by = 0  

          or        x2 + y2 – ax – b/2 y = 0                       …(1) 

Since the two chords are bisected by x-axis so let (h, 0) be the mid point where h has two real values. 

Equation of the chord is

                   T = S1  

                 

It passes through (ab/2)  

                

         

   

Since the value of h are real and distinct so

               B2 – 4AC > 0  

                     

                            

                                    

                          a2 – 2b2 > 0  

                          a2 > 2b2.

SIMILAR QUESTIONS

Q1

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5x + by – a = 0 passes through P and Q for:  

Q2

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Q3

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Q8

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Q9

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Q10

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