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The locus of the point of intersection of the tangents to the circle at points whose…
MATHEMATICS · Single correct · CBSE · Mathematics · Circles · Circles
Problem
The locus of the point of intersection of the tangents to the circle
x
=
r
cos
θ
,
y
=
r
sin
θ
x = r \cos \theta, y = r \sin \theta
x
=
r
cos
θ
,
y
=
r
sin
θ
at points whose parametric angles differ by
π
3
\frac{\pi}{3}
3
π
is (1)
x
2
+
y
2
=
4
(
2
−
3
)
r
2
x^2 + y^2 = 4(2 - \sqrt{3})r^2
x
2
+
y
2
=
4
(
2
−
3
)
r
2
(2)
3
(
x
2
+
y
2
)
=
1
3(x^2 + y^2) = 1
3
(
x
2
+
y
2
)
=
1
(3)
x
2
+
y
2
=
(
2
−
3
)
r
2
x^2 + y^2 = (2 - \sqrt{3})r^2
x
2
+
y
2
=
(
2
−
3
)
r
2
(4)
3
(
x
2
+
y
2
)
=
4
r
2
3(x^2 + y^2) = 4r^2
3
(
x
2
+
y
2
)
=
4
r
2
Related theory
Cartesian Coordinate System
Circles
Equation of a circle
Coordinate Geometry
Tangent length properties
Tangent to a circle
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