Question

The locus of the centre of the circle which cuts a chord of length 2a from the positive x-axis and passes through a point on positive y-axis distant b from the origin is.

• A. $x ^ { 2 } + 2 b y = b ^ { 2 } + a ^ { 2 }$
• B. $x ^ { 2 } - 2 b y = b ^ { 2 } + a ^ { 2 }$
• C. $x ^ { 2 } + 2 b y = a ^ { 2 } - b ^ { 2 }$
• D. $x ^ { 2 } - 2 b y = b ^ { 2 } - a ^ { 2 }$

Answer 1

Answer: (C)

$x ^ { 2 } + 2 b y = a ^ { 2 } - b ^ { 2 }$

Answer 2

Here $2 \sqrt { g ^ { 2 } - c } = 2 a \Rightarrow g ^ { 2 } - a ^ { 2 } - c = 0$ .....(i)

and it passes through (0, b), therefore

$b ^ { 2 } + 2 f b + c = 0$ ….(ii)

On adding (i) and (ii), we get $g ^ { 2 } + 2 f b = a ^ { 2 } - b ^ { 2 }$

Hence locus is $x ^ { 2 } + 2 b y = a ^ { 2 } - b ^ { 2 }$.