kaybaby said:Homework Statement
Find the equation of the plane that passes through the line of intersection of the planes 4x - 3y - z - 1 = 0 and 2x + 4y + z - 5 = 0 and parallel to the x - axis.
Homework Equations
The Attempt at a Solution
The equation of the plane: 4x+2kx-3y+k4y-z+kz-1-k5=0
do i then assume the plane parallel to the x-axis has points (1,0,0)?
then sub into the equation and solved k=-2
therefore the equation will be =-11y+3z-9?
The equation for a line that is parallel to the x-axis is y = c, where c is a constant value. This means that the line will have a constant y-value, no matter what the x-value is.
The intersection point of two lines that are parallel to the x-axis will have the same y-value, so you can set the two equations equal to each other and solve for x. This will give you the x-coordinate of the intersection point. The y-coordinate can be found by substituting the x-coordinate into either of the original equations.
No, two lines that are parallel to the x-axis will never intersect. This is because they have the same slope (which is 0) and will never cross each other.
A system of equations where both lines are parallel to the x-axis will have infinitely many solutions. This is because any point on the parallel lines will satisfy both equations.
No, the slope of a line parallel to the x-axis will always be 0, not undefined. This is because the slope is calculated by dividing the change in y-values by the change in x-values, but since the x-values are always the same for a line parallel to the x-axis, the change in x-values will be 0, resulting in a slope of 0.