Question

If $A( - a,0)$ and $B(a,0)$ are two fixed points, then the locus of the point on which the line AB subtends the right angle, is.

• A. $x^{2} + y^{2} = 2a^{2}$
• B. $x^{2} - y^{2} = a^{2}$
• C. $x^{2} + y^{2} + a^{2} = 0$
• D. $x^{2} + y^{2} = a^{2}$

Answer 1

Answer: (D)

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

Answer 2

We know that$P A ^ { 2 } + P B ^ { 2 } = A B ^ { 2 }$

$\Rightarrow ( x - a ) ^ { 2 } + y ^ { 2 } + ( x + a ) ^ { 2 } + y ^ { 2 } = ( 2 a ) ^ { 2 }$

$\Rightarrow x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$.