Locus of the point of intersection of the pair of perpendicular tangents to the circles x2+y2=1 and x2+ y2=7 is the director circle of the circle with radius equal to

Question

Locus of the point of intersection of the pair of perpendicular tangents to the circles x2+y2=1 and x2+ y2=7 is the director circle of the circle with radius equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/7a9aebf2c1b18f2af2f8286faf9d7477-.png" /> h2+k2=1+7 ∴ locus of the point P is x2+y2=8 This is the director circle of circle x2+y2=4 ∴ x2+y2=8 is director circle of a circle with radius =2.

Q. Locus of the point of intersection of the pair of perpendicular tangents to the circles $x^{2} + y^{2} = 1$ and $x^{2} +$ $y^{2} = 7$ is the director circle of the circle with radius equal to

$h^{2} + k^{2} = 1 + 7$
$∴$ locus of the point $P$ is
$x^{2} + y^{2} = 8$
This is the director circle of circle $x^{2} + y^{2} = 4$
$∴ x^{2} + y^{2} = 8$
is director circle of a circle with radius $= 2$ .

Q. Locus of the point of intersection of the pair of perpendicular tangents to the circles x2+y2=1 and x2+ y2=7 is the director circle of the circle with radius equal to

h2+k2=1+7 ∴ locus of the point P is x2+y2=8 This is the director circle of circle x2+y2=4 ∴x2+y2=8 is director circle of a circle with radius =2.

Q. Locus of the point of intersection of the pair of perpendicular tangents to the circles $x^{2} + y^{2} = 1$ and $x^{2} +$ $y^{2} = 7$ is the director circle of the circle with radius equal to

$h^{2} + k^{2} = 1 + 7$
$∴$ locus of the point $P$ is
$x^{2} + y^{2} = 8$
This is the director circle of circle $x^{2} + y^{2} = 4$
$∴ x^{2} + y^{2} = 8$
is director circle of a circle with radius $= 2$ .