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BITSAT 2024

Exam: BITSAT
Year: 2024
Subject: Mathematics
Chapter: Circle

BITSAT 2024 · Mathematics · Circle

The locus of the mid-point of a chord of the circle x^2+y^2=4 ,...

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

Options

A $x+y=2$
B $x^2+y^2=1$
C $x^2+y^2=2$
D $x+y=1$

Correct answer

C. $x^2+y^2=2$

Step-by-step solution

According to question,

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

In

\triangle O C B

,

\begin{aligned} & \cos 45^{{}^{\circ}}=\frac{\sqrt{h^2+k^2}}{2} \\ & \Rightarrow \quad \frac{\sqrt{h^2+k^2}}{2}=\frac{1}{\sqrt{2}} \\ & \Rightarrow \quad h^2+k^2=2 \end{aligned}

Replacing

h \rightarrow x

and

k \rightarrow y\text{ Locus } \Rightarrow x^2+y^2=2

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