Setting the distance between two points

[amathproblemthatneedsolve]

I'm not sure how to achieve this nor know if it's possible (I know it should be).

I have an equation of a parabola [MATH]y^2=\frac{128}{19}x[/MATH] and I have a line at x=9.5 I want the distance from x=9.5 to the parabola to = 3.6m

how do I achieve this? I have this graph if it helps.. https://www.desmos.com/calculator/39ppyiysk2

 

[Dr.Peterson]

I'm confused. The distance from that line to the parabola is 0, since they intersect.

Do you mean, perhaps, that you want to find points on the parabola that are 3.6 units from the line?

 

[amathproblemthatneedsolve]

I'm confused. The distance from that line to the parabola is 0, since they intersect.

Do you mean, perhaps, that you want to find points on the parabola that are 3.6 units from the line?

Yes my bad sorry poor wording

I meant, imagine that the x=9.5 is at the bottom(the ground) and the parabola is the top how would I find the point on the line where it reaches the roof and the distance is 3.6m

 

[Dr.Peterson]

Well, the distance of a point from a vertical line is just the difference in the x-coordinates, so that's still pretty easy. Just add or subtract 3.6 to 9.5.

 

[amathproblemthatneedsolve]

See my post #3 hopefully that makes sense

 

[Dr.Peterson]

I meant, imagine that the x=9.5 is at the bottom(the ground) and the parabola is the top how would I find the point on the line where it reaches the roof and the distance is 3.6m

Does that mean my guess in the last paragraph of #2 was right?

Do you mean, perhaps, that you want to find points on the parabola that are 3.6 units from the line?

If so, then just do the addition or subtraction I mentioned to find x, then plug that into the equation of the parabola and solve for y.

 

[Steven G]

I looked at your graph. So you want to draw a horizontal line from the graph curve (yes a line is a curve) to the red curve.

You know the x-value of the green curve, it is ___?

Now subtract 3.6 from that value to get the x-value of the red curve. Now use the equation of the red curve to compute the y-value(s). Post back showing your work