Hi,
Could some one explain how to find the intersection of parabola y^2=x with the line y = x/4
cheers
At the intersection point, the point is common to both curves. So the (x,y) of one is also the (x,y) of the other. Hence, solve the two equations simultaneously.
y^2 = x ---------(1)
y = x/4
4y = x -----------(2)
The x of (1) is also the x of (2), so,
y^2 = 4y
y^2 -4y = 0
y(y -4) = 0
y = 0 or 4
When y=0,
y^2 = x
0 = x
So, point (0,0)
When y = 4,
4^2 = x
x = 16
So, point (16,4)
Those two points are the intersections of the two curves (a parabola and a straight line).