A) 4
B) -4
C) Both [a] and [b]
D) 0
Correct Answer: C
Solution :
| According to the question, the distance between the points (4, p) and (1,0) = 5 |
| i.e. \[\sqrt{{{\left( 1-4 \right)}^{2}}+{{\left( 0-p \right)}^{2}}}=5\] |
| [\[\because\] distance between the points \[\left( {{x}_{1}},\,{{y}_{2}} \right)\]and \[\left( {{x}_{2}},\,{{y}_{2}} \right),d=\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}\]] |
| \[\Rightarrow \,\,\,\sqrt{{{\left( -3 \right)}^{2}}+{{p}^{2}}}=5\] |
| \[\Rightarrow \,\,\,\,\sqrt{9+{{p}^{2}}}=5\] |
| On squaring both the sides, we get |
| \[9+{{p}^{2}}=25\Rightarrow {{p}^{2}}=16\,\,\Rightarrow p=\pm 4\] |
| Hence, the required value of p is \[\pm \,4\]. |
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