Question

If the distance of the point A(x, y) from A(a, 0) be a+x, prove that y2 =4ax

Answer 1

distance between two points A(x1,y1) and B (x2,y2) = √(x1-x2)²+(y1-y2)²

⇒√(x-a)²+(y-0)²= a+x
⇒(x-a)²+y²=(a+x)²
⇒x²+a²-2ax+y²=a²+x²+2ax
⇒-2ax+y²=2ax
⇒y²=4ax

Answer 2

Answer:

Step-by-step

using the distance formula, √(x²-x)²+(y²-y)²

a+x = √(a-x)² + (√0-y)²

Squarring both sides,

we get,

(a+x)² = (a-x)² + (0-y)²

a²+2.a.x +x² = a² -2.a.x +x² +y²

or, 2ax = -2ax +y²

or, y²= 2ax + 2ax

or y² = 4ax

∴ proved