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NDA Math Circle

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Question : 10 of 26

Marks: +1, -0

A circle is drawn on the chord of a circle

x^2

y^2

a^2

as diameter. The chord lies on the line x+ y=a . What is the equation of the circle?

$x^2$ + $y^2$ - ax - ay + $a^2$ = 0
$x^2$ + $y^2$ - ax - ay =0
$x^2$ + $y^2$ + ax + ay
$x^2$ + $y^2$ + ax + ay -2 $a^2$ = 0

Solution:

(B)

Given equation of circle is

x^2

+

y^2=a^2

and equation of chord x+ y=a

For point of intersection eliminate y, we get

x^2

+

(a−x)^2=a^2

⇒ x=0, a

Hence intersection point A(0,a) and B(0, a)

Now circle with AB as diameter is

(x−0)(x−a)+( y−a)( y−0)=0

⇒

x^2

+

y^2

− ax−ay=0

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