JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
The set of all values of \(a^2\) for which the line \(x + y =0\) bisects two distinct chords drawn from a point \(P\left(\frac{1+a}{2}, \frac{1-a}{2}\right)\) on the circle \(2 x ^2+2 y ^2-(1+ a ) x -(1- a ) y =0\) is equal to:
- A \((8, \infty)\)
- B \((4, \infty)\)
- C \((0,4]\)
- D \((2,12]\)
Answer & Solution
Correct Answer
(A) \((8, \infty)\)
Step-by-step Solution
Detailed explanation
\(x ^2+ y ^2-\frac{(1+ a ) x }{2}-\frac{(1- a ) y }{2}=0\) \(\text { Centre }\left(\frac{1+ a }{4}, \frac{1- a }{4}\right) \Rightarrow( h , k )\) \(P \left(\frac{1+ a }{2}, \frac{1- a }{2}\right) \Rightarrow(2 h , 2 k )\) Equation of chord \(\Rightarrow T=S_1\)…
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