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Answer the question of the fiitjee package i am sending the pic of really challenging.the question r of circles Please I am begging.

Answer the question of the fiitjee package i am sending the pic of really challenging.the question r of circles 
Please I am begging.

Question Image
Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear student
 
Please ask ony ine question in one thread.
 
2.
 
Eqn of the chord AB of the circle : x² + y² = a². whose mid point is (h,k) is --- 

=> h x + ky = h² + k² 

(1) ∠ AOB = 90° , D is the mid point (h,k) 

=> AB = Sqrt ( a² + b²) = a . √2 , AD = (a/2) √2 = a/√2 

=> OD² = (1/4).2.a² 

=> h² + k² = a²/2 

=> x² + y² = a²/2 ………………. Answer 

(2) If the chord passes through a fixed point ( x₁ , y₁ )., then 

h. x₁ + k y₁ = h² + k² 

Hence the locus of the point in this case is --- 

x.x₁ + y.y₁ = x² + y² 

=

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