Question

The locus of the centre of the circle which cuts off intercepts of length $2 a$ and $2 b$ from x-axis and y-axis respectively, is.

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

Answer 1

Answer: (C)

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

Answer 2

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

$2 \sqrt { f ^ { 2 } - c } = 2 b$ ….(ii)

On squaring (i) and (ii) and then subtracting (ii) from (i), we get

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