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

Correct Answer is : x2²2 + y2²2 = 2

Correct Answer is : x2²2 + y2²2 = 2

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BITSAT 2019 Paper

Section: Mathematics

Question : 86 of 150

Marks: +1, -0

^2

^2

= 4 , which subtends a right angle at the origin is

Solution:

(c)

Equation of given circle is x

^2

+ y

^2

= 4

Its centre, 0 = (0,0) and radius, r = 2

Draw OM ⊥ AB

Clearly M is the mid-point of AB which subtends a right angle at O.

In ΔAOB, OA = OB radius

∴ ∠A = ∠B =

\frac{\pi}{4}

and in ΔOMA, sinA =

\frac{OM}{OA}

sin

\frac{\pi}{4}=\frac{OM}{2}

⇒

\frac{1}{\sqrt{2}}=\frac{OM}{2}

⇒

OM=\sqrt{2}

...(1)

Let M = (x, y) then OM =

\sqrt{x^2 + y^2}

...(2)

From (1) and (2),

x^2 + y^2

= 2

This is the required equation of locus.

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