Question

The locus of centres of circles which touch two intersection lines is a

• A. parabola
• B. ellipse
• C. straight line
• D. circle

Answer 1

The correct option is C straight line

In $△YXO$ and $△ZXO$

$\Rightarrow \angle OYX=\angle OZX={90}^{\circ }$

$\Rightarrow OX$ is common

$OY=OZ$ (radius)

$\Rightarrow △YXO\cong △ZXO$ (S-A-S congruency)

$\therefore \angle YXO=\angle ZXO$

So, the Locus of the centers is a straight line bisecting them between two intersecting lines.