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## Homework Statement

the line goes through (0, 3/2) and is orthogonal to a tangent line to the part of parabola y = x^2, x > 0

## Homework Equations

## The Attempt at a Solution

I have problems regarding finding the equation of tangent line to the part of parabola

because the question not specifically mention at which point

we know that the tangent line (y2) tangent to the part of parabola

so, the slope of y2 = the slope of parabola at (x,y)

parabola y = x^2

so the slope is 2x

and the slope changes according to x

which x should I used for x > 0?

if I use x = 1, y = 1^2= 1, slope = 2

and the y2 would be

y - 1 = 2(x - 1)

y = 2x - 1

but if I used x = 3, y = 9, slope = 6

and the y2 would be

y - 9 = 6(x-3)

y = 6x - 9

and y2 is different for each x...

I need to find the slope of y2, so I can find the line equation orthogonal to y2 passing through (0, 3/2) ...