If the distance of the point P(x, y) from A(a, 0) is \(a+x\), then \(y^2\) equals:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4ax
Write the distance PA with the distance formula, set it equal to \(a+x\), and square both sides to remove the square root.
By the distance formula, \(PA=\sqrt{(x-a)^2+(y-0)^2}=a+x\)
Squaring both sides removes the root: \((x-a)^2+y^2=(x+a)^2\)
The difference of the two squares is \(4ax\), so \(y^2=(x+a)^2-(x-a)^2=4ax\)