JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
A circle passing through the point \(P (\alpha, \beta)\) in the first quadrant touches the two coordinate axes at the points \(A\) and \(B\). The point \(P\) is above the line \(A B\). The point \(Q\) on the line segment \(A B\) is the foot of perpendicular from \(P\) on \(A B\). If \(P Q\) is equal to \(11\) units, then the value of \(\alpha \beta\) is \(.............\).
- A \(120\)
- B \(122\)
- C \(123\)
- D \(121\)
Answer & Solution
Correct Answer
(D) \(121\)
Step-by-step Solution
Detailed explanation
Let equation of circle is \((x-a)^2+(y-a)^2=a^2\) which is passing through \(P (\alpha, \beta)\) then \((\alpha-a)^2+(\beta-a)^2=a^2\) \(\alpha^2+\beta^2-2 \alpha a-2 \beta a+a^2=0\) Here equation of \(AB\) is \(x + y = a\) Let \(Q\left(\alpha^{\prime}, \beta^{\prime}\right)\)…
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