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The locus of the middle points of chords of the
circle $x^{2} + y^{2} = 25$ which are parallel to the line $x - 2 y + 3 = 0$ is

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x+2y=0

2x+y=0

x−2y=0

2x−y=0

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detailed solution

Correct option is B

Let (h,k) be the mid-point of a chord of the circlex2+y2=25 Then, equation of the chord ishx+ky−25=h2+k2−25⇒hx+ky=h2+k2If this is parallel to x−2y+3=0, then −hk=12⇒2h+k=0So, the locus of (h,k) is 2x+y=0

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The locus of the middle points of chords of the circle x2+y2=25 which are parallel to the line x−2y+3=0 is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The locus of the middle points of chords of the
circle $x^{2} + y^{2} = 25$ which are parallel to the line $x - 2 y + 3 = 0$ is