Locus of the point of intersection of perpendicular tangents to the circle x2 + y2 = 16

Question

Locus of the point of intersection of perpendicular tangents to the circle x2 + y2 = 16  (A)  x2 + y2 = 8  (B)  x2 + y2 = 32  (C)  x2 + y2 = 64  (D)  x2 + y2 = 16

Tardigrade Admin · Accepted Answer

We know that, if two perpendicular tangents to the circle x2+y2=a2 meet at P, then the point P lies on a director circle. ∴ Required locus is x2+y2=32

Q. Locus of the point of intersection of perpendicular tangents to the circle $x^{2} + y^{2} = 16$

$x^{2} + y^{2} = 8$

$x^{2} + y^{2} = 32$

$x^{2} + y^{2} = 64$

$x^{2} + y^{2} = 16$

We know that, if two perpendicular tangents to the circle $x^{2} + y^{2} = a^{2}$ meet at $P$ , then the point $P$ lies on a director circle.
$∴$ Required locus is $x^{2} + y^{2} = 32$

Q. Locus of the point of intersection of perpendicular tangents to the circle x2+y2=16

x2+y2=8

x2+y2=32

x2+y2=64

x2+y2=16