You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Chord of Contact

Let C be the ...

Question

Let $C$ be the circle with centre $(0, 0)$ and radius $3$ units. Locus of the point $P$ from which the chord of contact subtends an angle of $60^{\circ}$ at any point on the circumference of $C$ is

x^{2} + y^{2} = 27

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} + y^{2} = 18

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} + y^{2} = 36

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $x^{2} + y^{2} = 36$
$C : x^{2} + y^{2} = 9$

In triangle $O A B$ ,
$A B = (2 sin 60^{\circ}) O A$

$\Rightarrow \frac{2 (\sqrt{h^{2} + k^{2} - 9}) \cdot 3}{\sqrt{h^{2} + k^{2}}} = \frac{3 \cdot 2 \cdot \sqrt{3}}{2} [From △ O A P]$
$\Rightarrow 4 (h^{2} + k^{2} - 9) = 3 (h^{2} + k^{2})$
$\Rightarrow h^{2} + k^{2} = 36$

Hence, locus is $x^{2} + y^{2} = 36$ .

Suggest Corrections

Similar questions

Q. Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the midpoints of the chords of the circle C that subtend an angle of

\frac{2 π}{3}

at its centre is

Let $C$ be the circle with centre $(0, 0)$ and radius $3$ units. Locus of the point $P$ from which the chord of contact subtends an angle of $60^{\circ}$ at any point on the circumference of $C$ is

Q. STATEMENT - 1 : Locus of mid point of chords of circle

x^{2} + y^{2} = 4

which subtends angle of

\frac{π}{2}

at origin is

x^{2} + y^{2} = 1.

STATEMENT - 2 : If any chord of circle

x^{2} + y^{2} = r^{2}

subtends an angle

^{'} θ^{'}

at center, then its mid point always lies on

x^{2} + y^{2} = r^{2} {cos}^{2} (\frac{θ}{2})

Q. The locus of the point, whose chord of contact w.r.t the circle

x^{2} + y^{2} = a^{2}

makes an angle

2 α

at the centre of the circle is

List- I	List- II
A. The locus of the point of intersection of the perpendicular tangents of $x^{2} + y^{2} = a^{2}$	1) $x^{2} + y^{2} = 5$ of
B. The locus of the mid-point of the chord of the circle $x^{2} + y^{2} = 8$ which is $\sqrt{2}$ units from origin is	2) $x^{2} + y^{2} = a^{2} {sec}^{2} α$
C. The locus of the point of intersection of the lines $x = \frac{1 - t^{2}}{1 + t^{2}}$ and $y = \frac{2 t}{1 + t^{2}}$	3) $x^{2} + y^{2} = 2 a^{2}$
D. The locus of the point whose chord of contact w.r.t $x^{2} + y^{2} = a^{2}$ making an angle '2 $α$ ' at the center is	4) $x^{2} + y^{2} = 2$ 5) $x^{2} + y^{2} = 1$

Join BYJU'S Learning Program

Let C be the circle with centre (0,0) and radius 3 units. Locus of the point P from which the chord of contact subtends an angle of 60∘ at any point on the circumference of C is

The correct option is C x2+y2=36C:x2+y2=9 In triangle OAB, AB=(2sin60∘)OA ⇒2(√h2+k2−9)⋅3√h2+k2=3⋅2⋅√32 [From △OAP] ⇒4(h2+k2−9)=3(h2+k2) ⇒h2+k2=36 Hence, locus is x2+y2=36.

Let $C$ be the circle with centre $(0, 0)$ and radius $3$ units. Locus of the point $P$ from which the chord of contact subtends an angle of $60^{\circ}$ at any point on the circumference of $C$ is