SATHEE: Circle 5 Question 6

Circle 5 Question 6

6. The locus of the mid-point of a chord of the circle $x^{2} + y^{2} = 4$ which subtends a right angle at the origin, is

(a) $x + y = 2$

(b) $x^{2} + y^{2} = 1$

(1984, 2M)

(d) $x + y = 1$

Objective Question II

(One or more than one correct option)

Show Answer

Answer:

Correct Answer: 6. (c)

Solution:

We have to find locus of mid-point of chord and we know perpendicular from centre bisects the chord.

$∴ ∠ O A C = 45^{\circ}$

In $△ O A C$ ,

$\frac{O C}{O A} = \sin 45^{\circ}$

$\Rightarrow O C = \frac{2}{\sqrt{2}} = \sqrt{2}$

Also,

$\sqrt{h^{2} + k^{2}} = O C^{2}$

Hence, $x^{2} + y^{2} = 2$ is required equation of locus of mid-point of chord subtending right angle at the centre.

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Circle 5 Question 6

6. The locus of the mid-point of a chord of the circle x2+y2=4 which subtends a right angle at the origin, is

Objective Question II

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6. The locus of the mid-point of a chord of the circle $x^{2} + y^{2} = 4$ which subtends a right angle at the origin, is