If the length of transverse common tangent of the circles x2+y2=1 and (x-h)2+y2=1 is 2 √3, then the value(s) of h will be

Question

If the length of transverse common tangent of the circles x2+y2=1 and (x-h)2+y2=1 is 2 √3, then the value(s) of h will be (A) 2 (B) -2 (C) ± 4 (D) None of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/2a2061b99036f96c43b9ab57b48dc46a-.png" /> Since radius of both the circles is same, coordinates where it cuts the line joining their centers is (h / 2,0) C1 O2+O P2=C1 P2 or 1+3=h2 / 4 or h2=16 or h=± 4

Q. If the length of transverse common tangent of the circles $x^{2} + y^{2} = 1$ and $(x - h)^{2} + y^{2} = 1$ is $23$ , then the value(s) of $h$ will be

2

$- 2$

$\pm 4$

None of these

Since radius of both the circles is same, coordinates where it cuts the line joining their centers is $(h /2, 0)$
$C_{1} O^{2} + O P^{2} = C_{1} P^{2}$
or $1 + 3 = h^{2} /4$
or $h^{2} = 16$
or $h = \pm 4$

Q. If the length of transverse common tangent of the circles x2+y2=1 and (x−h)2+y2=1 is 23​, then the value(s) of h will be

2

−2

±4

None of these

Since radius of both the circles is same, coordinates where it cuts the line joining their centers is (h/2,0) C1​O2+OP2=C1​P2 or 1+3=h2/4 or h2=16 or h=±4

Q. If the length of transverse common tangent of the circles $x^{2} + y^{2} = 1$ and $(x - h)^{2} + y^{2} = 1$ is $23$ , then the value(s) of $h$ will be

$- 2$

$\pm 4$

Since radius of both the circles is same, coordinates where it cuts the line joining their centers is $(h /2, 0)$
$C_{1} O^{2} + O P^{2} = C_{1} P^{2}$
or $1 + 3 = h^{2} /4$
or $h^{2} = 16$
or $h = \pm 4$