Calculus

posted by .

Find an equation of the line through the point (3,5) that cuts off the least area from the first quadrant.

How do I solve? I am stuck. The only thing I can come with is this:

y-5=m(x-3)

How to use this I don't know.

• Calculus -

draw a line through (3,5) cutting the positive x and y axes at (a,0) and (0,b)

then the area of the triangle is
A = ab/2

but the slope of the two segments must be equal, so 5/(3-a) = (b-5)/-3
solving for b gave me b = 5a/(a-3)

then A = 5a^2/(2a-6)
using the quotient rule
dA/da = [(2a-6)(10a) - 5a^2(2)]/(2a-6)^2
= 0 for a max/min of A

simplifying the top and setting it equal to zero gave me
a^2 - 6a = 0
a(a-6)=0
a = 0 or a = 6
clearly a=0 does not give me a triangle, so a = 6 and b= 10
so slope = 5/-3
y-5 = (-5/3)(x-3)

take it from there.

• Calculus -

how did you get the slope of the two lines? I get everything else though.

• Calculus -

there is only one line
you were given the point (3,5) and I found
the x-intercept to be (6,0)
so slope = (5-0)/(3-6)
= 5/-3 = - 5/3

Similar Questions

1. Calculus

I asked for help on a question yesterday and I got really good help and I was wondering if someone could help with this problem too. This is the question: Find an equation of the line through the point (1,3) that cuts off the least …
2. Equation of a straight line.

1. Find the equation of the line described in each case: a) Gradient 3, cuts through (0, 6). b) Steepness of 4, passes through (0, -2). c)Parallel to y = 5x - 1, cuts the y-axis at (0, 10). d)Cuts through (0, 7) and (5, 17) 2. Here …
3. math

Find an equation of the line through the point that cuts off the least area from the first quadrant. Please enter your answer in the slope-intercept form. What were the coordinates of the point?
4. Calculus

PLEASE HELP Find the equation of the line through the point (3,4) which cuts from the first quadrant a triangle of minimum area.

Find the equation of the line through the point (3,4) which cuts from the first quadrant a triangle of minimum area.
6. calculus HELP URGENT

Find the equation of the line through the point (3,4) which cuts from the first quadrant a triangle of minimum area.
7. calculus

At what point on the parabola y = 1-x^2 does the tangent have the property that it cuts from the first quadrant a triangle of minimum area?
8. Math

A straight line x/a -y/b =1 passes through the point (8,6) and cuts off a triangle of area 12 units from the axes of coordinates .find the equation of straight line
9. Calculus

Find the equation of the line through the point (3, 5) that cuts off the least area from the first quadrant?
10. Calculus

Find the slope and y-intercept of the line through the point (6,2) that cuts off the least area from the first quadrant.

More Similar Questions