NIMCET 2010 — Mathematics PYQ

1. Analyze the first circle ($C_1$):

Equation: $x^2+y^2=9$

• Center ($C_1$): $(0,0)$

• Radius ($r_1$): $\sqrt{9}=3$

2. Analyze the second circle ($C_2$):

Equation: $x^2+y^2-6x-8y+25=c^2$

To find the center and radius, we complete the square:

$(x^2-6x+9)+(y^2-8y+16)=c^2-25+9+16$

$(x-3{)}^2+(y-4{)}^2=c^2$

• Center ($C_2$): $(3,4)$

• Radius ($r_2$): $|c|$ (since $c^2$ is the radius squared, $r=c$ assuming $c$ is positive as per options).

3. Calculate the distance ($d$) between centers:

4. Apply the containment condition:

For $C_1$ to be contained in $C_2$:

Conclusion:

Looking at the given options, only (d) $c=10$ satisfies the condition $c\ge 8$.

Correct Option: (d)