Question

A point P moves so that its distance from the point $(a,0)$ is always equal to its distance from the line $x + a = 0$. The locus of the point is.

• A. $y^{2} = 4ax$
• B. $x^{2} = 4ay$
• C. $y^{2} + 4ax = 0$
• D. $x^{2} + 4ay = 0$

Answer 1

Answer: (A)

$y^{2} = 4ax$

Answer 2

$( x - a ) ^ { 2 } + y ^ { 2 } = ( x + a ) ^ { 2 } \Rightarrow y ^ { 2 } = 4 a x$

Note : This is also the definition of parabola $y ^ { 2 } = 4 a x$