# lines

1. ### Planes and Lines I

There are four problems I need to know how to solve before an exam and I just can't. I was hoping that I could get some help here! Question 1: A point is mirrored in the line 4x + 3y = 0. The position of the mirrored point is (-5, 3). What is the position of the original point?
2. ### find the angle between two lines formed by three points in n-space

Hello, I wasn't sure where to post this, so please feel free to move it. In some ways, I suspect this is a very elementary question for an expert, so I posted in on the pre-university side. Here is an example in 2D of the problem I am looking at, given three sets of coordinates...
3. ### Linear functions: Perpendicular lines.

Hey i need help with number 14 and 15. I know that the slope has to be -1 in order for the line to perpendicular.
4. ### Find the Distance between two parallel Lines

how to use the equation D=c1-c2/(A)^2+(B)^2 in this given question : 4x+y=6 12x+3y=14 i know how to use it on same A and B like this 3x+12y-4=0 3x+12y+15=0 but in the another given im confused
5. ### Tangent lines

Hello, Determine the equations of the tangent lines to the graph of f(x)=3x(5x^2+1) that are parallel to the line y=8x+9 This is what I have so far: d/dx(3x(5x^2+1))=45x^2+3 45x^2+3=8 x=-1/3, x=1/3 When I sub this into my formula I get f=-14/9 and f=14/9. does this seem right?
6. ### Equations of tangent lines question

1. Determine the equations of the tangent lines to the graph of f(x)=3x(5x^2+1) that are parallel to the line y=8x+9. Sketch a graph of the function, the tangent lines, and the line y=8x+9. I know that the derivative of f(x)=3x(5x^2+1) is f'(x)=45x^2+3, but I don't know where to go from there...
7. ### Horizontal lines.

Hi so I checked my answers, I got all of my problems right, but I do not know 2 of them. Okay so the first problem is : (7,-6) it said "find the equation of the horionztal line passing through (7,-6) so I put the answer -6 second problem: "find the equation of the horizontal passing through...
8. ### Find Tangent Line(s)

Find the tangent line(s) to the curve y = x^3 - 9x through the point (1, -9). My Work: y = x^3 - 9x y' = 3x^2 - 9 I then thought about evaluating at x = 1. Afterward, I got y' = -6. I have my point and slope. I quickly thought about the point-slope formula. y - y_1 m(x...
9. ### Finding parallel lines

Question: Find the value of a so that the lines y=3-(1/2)x and ay+3x=4 are parallel So if the slope of y=3-(1/2)x is -1/2 then I know that the other line has to have the same slope in order to be parallel. Rearranging the equation I get y=(4-3x)/a. I was thinking that a should be 6, so I'd get...
10. ### Equations of Tangent Lines

I need help with 48.
11. ### Distance Between Lines

Find the distance between the point and line, or between the lines, using the formula for the distance between the point (x,y) and the line Ax + By + C = 0. Let D be distance. D = |Ax + By + C|/sqrt{A^2+B^2} Given Lines: x + y = 1 x + y = 5 No point is given.
12. ### find the angle between two skew lines

I'm trying to find the angle between two skew lines. (See attached) I am doing a wheel alignment on a car I have drawn two lines of equal length that go from the centre of the wheel straight out in front of the car. Then work out the distance the two line are apart at two separate points. I...
13. ### curves, surfaces and tangent lines

Could someone please assist with the following questions: Consider $f(x,y) = x^{\frac{1}{3}}y^{\frac{1}{3}}$ and take $C$ to be the curve of intersection of $z = f(x,y)$ with the plane $y=x$. Show that the curve $C$ has a tangent line at the origin? I have tried showing that the directional...
14. ### Vectors - lines and planes (again)

Wow, these questions are really beginning to bother me, everything else in my syllabus and past papers are a breeze until i get to a vectors question... Anyway, my question is: Find a vector equation of the line through (4,2, -3), parallel to the line of intersection of the planes 3x - 2y =6...
15. ### Lines and plane

Been stuck on this one for quiet a while. Dont know where I should begin so I can solve s and t.
16. ### How to evaluate solid angle subtended by a finite plane bounded by straight lines

How to calculate solid angle (in Ste-radian) subtended by a plane bounded by the straight lines x=-8, x=12, y=-6 & y=20 in XY-plane at the point (8, -10, -6). Any help is highly appreciated. thanks ................... (Flower)(Flower)(Flower)
17. ### Determing the equation of the two tangent lines

The question is: Determine the equation of both lines that are tangent to the graph of y= x^2 +4 and pass through the point (1,-2) This is what I've managed to do so far. Not sure where to go from here.

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19. ### Calculus problem involving horizontal tangent lines?

Consider the following three curves: 1. y=sinx+cos2x-sin3x+7x-5 2. y=(1/5)x^5-(4/3)x^3+8x-5 3. y= e^(x^46)+3x^25+35x+15 Which of the three curves have at least one horizontal tangent line? I think I have to apply Rollie's theorem here, which says when f(a)=f(b), f'(c)=0, when a<c<b. But it...
20. ### Two lines intersect at P, find coordinates of P?

Hello, I am working on a set of problems. I don't quite even know where to begin. Any help would be greatly appreciated. Two lines with equations r1= (2,3,-1)+s(5,-3,2) and r2= (9,2,2)+t(-3,5,-1) intersect at the point P. Find coordinates of P.