calculus
posted by c .
Determine the coordinates of the point of intersection of the two perpendicular lines that intersect on the yaxis and are both tangent to the parabola given below.
y = 3x2

let y=mx+b be the first line
and y=1/m x+ d be the second line.
If y=3x^2 is tangent, then m=3, or m=1/3
.
y=3x^2=mx+b so m=3, b=0
y= 1/3 x +d, so m=1/3, d=0 
oops. one of them has to be negative, so y=1/3 x+ d, m=1/3, d=0

Since the two tangents are mutually perpendicular and intersect on the yaxis they have gradients 1 and 1
The gradient function is y = 6x
Hence x = 1/6, 1/6
So y = 1/12 both times
So the coordinate of the intercept can be calculated using the equation of the tangents:
Equate y  1/12 = x  1/6
and y  1/12 = 1(x + 1/6)
BUT you do not even have to do this!
Rewrite one of the equations in the form
y = mx + c to get the yintercept.
The coordinate required is
(0, 1/12)
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