The locus of the center of a variable circle which always touches two given circles externally is

Question

The locus of the center of a variable circle which always touches two given circles externally is (A) an ellipse (B) a hyperbola (C) a parabola (D) a circle

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/ba047f706ccee0ff24b6366a1af00120-.png" /> O O1=r+r1 O O2=r+r2 ∴ O O2-O O1=r2-r1 hence, locus is hyperbola

Q. The locus of the center of a variable circle which always touches two given circles externally is

an ellipse

a hyperbola

a parabola

a circle

$O O_{1} = r + r_{1}$
$O O_{2} = r + r_{2}$
$∴ O O_{2} - O O_{1} = r_{2} - r_{1}$
hence, locus is hyperbola

Q. The locus of the center of a variable circle which always touches two given circles externally is

an ellipse

a hyperbola

a parabola

a circle

OO1​=r+r1​ OO2​=r+r2​ ∴OO2​−OO1​=r2​−r1​ hence, locus is hyperbola

$O O_{1} = r + r_{1}$
$O O_{2} = r + r_{2}$
$∴ O O_{2} - O O_{1} = r_{2} - r_{1}$
hence, locus is hyperbola