JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let the equation \(x^{2}+y^{2}+p x+(1-p) y+5=0\) represent circles of varying radius \(\mathrm{r} \in(0,5]\). Then the number of elements in the set \(S=\left\{q: q=p^{2}\right.\) and \(\mathrm{q}\) is an integer \(\}\) is ..... .
- A \(60\)
- B \(61\)
- C \(62\)
- D \(63\)
Answer & Solution
Correct Answer
(B) \(61\)
Step-by-step Solution
Detailed explanation
\(r=\sqrt{\frac{\mathrm{p}^{2}}{4}+\frac{(1-\mathrm{p})^{2}}{4}-5}=\frac{\sqrt{2 \mathrm{p}^{2}-2 \mathrm{p}-19}}{2}\) Since, \(r \in(0,5]\) So, \(0\,<\,2 \mathrm{p}^{2}-2 \mathrm{p}-19\, \leq 100\)…
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