Posted by **albian** on Friday, August 28, 2009 at 8:40pm.

consider the line y=6x-k and the parabola y=x^2

i) for what value of k is the line y=6x-k a tangent to the parabola y=x^2 ?

ii) the line y=6x-k intersects the parabola in two distinct places. what is the largest integer value that k can take ?

- maths -
**bobpursley**, Friday, August 28, 2009 at 9:43pm
i. at x=3, the slope of the parabola is 6, so at 3, the parabola has a y value of 9, which means if the line y=6x+k is =9, then k=....

- maths -
**Reiny**, Friday, August 28, 2009 at 9:50pm
i)

using Calculus, this is easy

if y = x^2

dy/dx = 2x

but the slope of the line is 6

so 2x = 6

x = 3

if x=3 then y=9 from the parabola

so the point (3,9) must also be on the line

9 = 6(3)-k

k = 9

ii) let's intersect

y = x^2 and y = 6x-k

then x^2 - 6x + k = 0

to have 2 distinct roots, the discriminat must be positive

so b^2 - 4ac > 0

36 - 4(k) > 0

k < 9

since k=9 produces the tangent, and you asked for the largest integer that k could have,

k = 8

(strange question!)

## Answer this Question

## Related Questions

- calculus - The line x=c where c>0 intersects the cubic y=2x^(3)+3x^(2)-9 at ...
- math - The line x=c where c>0 intersects the cubic y=2x^(3)+3x^(2)-9 at point...
- math - Consider the parabola y = 7x - x2. (a) Find the slope of the tangent line...
- precalculus - graph the parabola y=2x^2-6x-3. plot point on the parabola A[1,-7...
- Math - If f(x)=3x^2-5x, find the f'(2) & use it to find an equation of tangent ...
- calculous - Find the area of the region bounded by the parabola y = 4x^2, the ...
- calculous - Find the area of the region bounded by the parabola y = 4x^2, the ...
- calculus - Find the area of the region bounded by the parabola y=x^2 , the ...
- calculusiii - he paraboloid z = 4 − x − x2 − 2y2 intersects ...
- math - A parabola has the equation y = 4(x-3)^2-7 Choose 2 true statements: A) ...