Notifications
Clear all
0
05/01/2022 1:28 pm
Topic starter
If x2 + y2 + px + y(1 - p) = 0 is the equation of circle, r ∈ (0,5], q = p2 then number of integral values of (p, q) satisfy is
(a) 16
(b) 14
(c) 19
(d) 21
1 Answer
0
05/01/2022 1:35 pm
Correct answer: (b) 14
Explanation:
Let S : x2 + y2 + px + y(1 - p) = 0
r = \(\sqrt{(\frac{p}{2})^2 + (\frac{1-p}{2})^2}\)
0 < \(\frac{p^2 + (1-p)^2}{4}\) ≤ 25
⇒ 0 < 2p2 + 1 - 2p ≤ 100
⇒ 0 < 2p2 - 2p + 1 ≤ 100
⇒ \(\frac{-1}{4}\) < \((p - \frac{1}{2})^2\) ≤ \(\frac{199}{4}\)
⇒ \((p - \frac{1}{2})^2\) ≤ \((\frac{\sqrt{199}}{2})^2\)
Total number of integral pairs of (p, q) = 14