Question:
The external centre of similitude for circles
\[
x^2+y^2+10x-16y-11=0
\]
and
\[
x^2+y^2-2x+4y-4=0
\]
is
The external centre of similitude for circles
\[
x^2+y^2+10x-16y-11=0
\]
and
\[
x^2+y^2-2x+4y-4=0
\]
is
Show Hint
For center of similitude, first convert circles into center-radius form and use section formula carefully.
Updated On: Jun 15, 2026
- \(\left(\frac57,-\frac47\right)\)
- \((-2,3)\)
- \(\left(\frac{25}{7},-\frac{44}{7}\right)\)
- \((-3,5)\)
Show Solution
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The Correct Option is C
Solution and Explanation
Concept:
External center divides line joining centers externally in ratio of radii.
Step 1: Find centers and radii.
Circle 1: \[ C_1=(-5,8) \] Radius \[ r_1=\sqrt{25+64+11} \] \[ r_1=10 \] Circle 2: \[ C_2=(1,-2) \] Radius \[ r_2=\sqrt{1+4+4} \] \[ r_2=3 \]
Step 2: Apply external division formula.
Point dividing externally in ratio \(10:3\) \[ x= \frac{10(1)-3(-5)}{10-3} \] \[ =\frac{10+15}{7} \] \[ =\frac{25}{7} \] \[ y= \frac{10(-2)-3(8)}{10-3} \] \[ =\frac{-20-24}{7} \] \[ =-\frac{44}{7} \] Hence \[ \boxed{\left(\frac{25}{7},-\frac{44}{7}\right)} \]
Step 1: Find centers and radii.
Circle 1: \[ C_1=(-5,8) \] Radius \[ r_1=\sqrt{25+64+11} \] \[ r_1=10 \] Circle 2: \[ C_2=(1,-2) \] Radius \[ r_2=\sqrt{1+4+4} \] \[ r_2=3 \]
Step 2: Apply external division formula.
Point dividing externally in ratio \(10:3\) \[ x= \frac{10(1)-3(-5)}{10-3} \] \[ =\frac{10+15}{7} \] \[ =\frac{25}{7} \] \[ y= \frac{10(-2)-3(8)}{10-3} \] \[ =\frac{-20-24}{7} \] \[ =-\frac{44}{7} \] Hence \[ \boxed{\left(\frac{25}{7},-\frac{44}{7}\right)} \]
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