calculus

posted by c

Determine the coordinates of the point of intersection of the two perpendicular lines that intersect on the y-axis and are both tangent to the parabola given below.
y = 3x2

1. bobpursley

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

2. bobpursley

oops. one of them has to be negative, so y=-1/3 x+ d, m=-1/3, d=0

3. Louis

Since the two tangents are mutually perpendicular and intersect on the y-axis 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!
Re-write one of the equations in the form
y = mx + c to get the y-intercept.
The coordinate required is
(0, -1/12)

Similar Questions

ok, I totally did not get this question at all. Complete each statement. Assume the variable a does not equal 0. a. The graph of y=ax^2+c intersects the x-axis in two places when ______. b. The graph of y=ax^2+c does not intersect …
2. Calculus

Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations. …
3. Vectors

I am really lost and confused! Consider the lines r = (1,-1,1) + t(3,2,1) and r = (-2,-3,0) + u(1,2,3). a) Find their point of intersection. b) Find a vector equation for the line perpendicular to both of the given lines that passes …
4. calculus

f(x)=kx^2+3 a) if the tangent lines to the graph of f at (t,f(t)) and (-t, f(-t)) are perpendicular, find t in terms of k b) Find the coordinate of the point of intersection of the tangent lines mentioned in part (a) in terms of k
5. maths

The parabola y2 = 4ax, where a > 0, and the rectangular hyperbola xy = C2, where C > 0, intersect at right angles. Show that the tangent and normal to either curve at the point of intersection meet the x-axis at T and N where …
6. calculus

A parabola ,f, intersect the x axis at A and B and the y axis at C. The axis of symmetry of the parabola has the equation x=-3.The line through A and C has the equation g(x)=x+7. Determine the coordinates of A,B and C
7. Calculus

At what point does the normal to y=-5-1x+3x^2 at (1, -3 ) intersect the parabola a second time?
8. Calculus

Draw a diagram to show that there are two tangent lines to the parabola y=x^2 that pass through the point (0,-4). Find the coordinates of the points where these tangent lines intersect the parabola. So far I have taken the derivative …
9. math

Draw a diagram to show that there are two tangent lines to the parabola y = x2 that pass through the point (0, −25). Find the coordinates of the points where these tangent lines intersect the parabola.
10. Calculus

I found part B, but stuck on part A. Use implicit differentiation to find the points where the parabola defined by x^2-2xy+y^2+4x-8y+24= 0 has horizontal and vertical tangent lines. A) The parabola has horizontal tangent lines at the …

More Similar Questions