Consider the line y = ax , where a is a positive constant. What is the shorteşt. distance between the line and the point (a, 0) ? (b). (c)- Ja+1 (d). la²+1 (a) 교+1 a²+1

Q: (d). Consider the line y = ax , where a is a positive constant. What is the shortest distance…

A:

Q: find the distance from the point to the line. (0, 0, 12); x = 4t, y = -2t, z = 2t

A:

Q: ub-) Find the equation of a line entirely in n which is perpendicular to the line D at the point…

A: You asked to solve part (b) only. So I supposed that you have equation of the plane π and…

Q: Where is the line y = 10 – 2x closest to the origin? (х, у) %3D

A:

Q: Suppose there is a straight line from z1 = 0 to z2 = 2 + 4i You know that the equation of a straight…

A:

Q: What are lines are perpendicular to the line 3x+2y=6

A: Line perpendicular to ax + by + c = 0 can be written as bx - ay + k = 0 , k= constant.   So line…

Q: What is the distance between the line with Cartesian equation x-4 = y-6 = z and the line with…

A:

Q: When is the line ax+ by = c parallel to the y-axis? To the x-axis?

A: ax+by+c=0        When a=0, then the line equation becomes               bx+c=0…

Q: Find the distance between the point (-3, 1, 5) and the line given by x = 5+t, y = 1- 2t, and z = 3-…

A: Given : Point A ( -3,1,5) x = 5+t  y=1-2t  z=3-t

Q: The diagonals of rhombus TEAM intersect at P(2,1). If the equation of the line that contains…

A:

Q: The slope of the line tangent to the graph of 3x +5In y 12 at (2, 1) is 12 (A) 12 (B) 5. (C) 12 4.

A: Given that 3x2+5lny=12To find : Slope of the tangent line at point 2,1Solution :

Q: Find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 + 4t

A: To find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 +…

Q: Suppose there is a straight line from z1 = 0 to z2 = 2+4i You know that the equation of a straight…

A:

Q: Find distance from the point (0, 1, 3) to the line = 2t, y = 6–2t, z = 3+t

A: (0,1,3)    L=x=2t, y=6-2t, z=3+t

Q: The equation of the line is of the form y=mx. what is the value of m ?

A:

Q: Which of r = 2 sec θ and r = 2 csc θ defines a horizontal line?

A: we have to tell which of r = 2 sec θ and r = 2 csc θ defines a horizontal line.

Q: Based on the trapezoid shown in the standard (x, y) coordinate plane above, what is the slope of the…

A: Here ABCD is a trapezoid and AB parallel BC which also parallel to the X axis

Q: Consider the line 3x – 2y = 7. What are the coordinates of the y-intercept for this line?

A: Consider the given equation of the line. 3x - 2y =7 At y intercept, x coordinate is zero.

Q: Find the distance from the point P(2,1) to the line v = x + 2

A:

Q: find the distance from A(4, 6, -3) to the line x = 3t + 1, y = -t + 3, z = 6t

A:

Q: What is the distance between the line with Cartesian equation x-6 = y-7 = z and the line with…

A: Parallel lines have the same direction ratios.

Q: Consider the line y = ax , where a is a positive constant. What is the shortest distance between the…

A:

Q: Thus, to find the slope of the secant line passing through P(2, 4) and Q(3, 3.), substitute x for x…

A: Topic:- Coordinate Geometry

Q: Find the distance of the point (4, 2, -4) from the line r(t) = (1+2t, 1+ 2t, 7 - 3t).

A:

Q: The line y = kr + 4, where k is a constant, is graphed in the xy-plane. If the line contains the…

A: Given line is: y = kx + 4 ................... (1) The line contains the point (c, d). Then (c, d)…

Q: * Let LIEX-54+10=D0 L2=4X+y-1-O be two lines. 1 Show that the lines L and Lz are not parallel.

A:

Q: Find the value of x for which line a is parallel to line b.

A: It is given that,  line a and b are parallel lines,

Q: Consider the line y = ax, where a is a positive constant. What is the shortest distance between the…

A: Given:- Consider the line y = ax, where a is a positive constant. To find:- What is the shortest…

Q: 2)What line is perpendicular to 2x + y = 3 at (1,1)?

A: What line is perpendicular to 2x+y=3 at (1,1)?

Q: In triangular space it is sufficient to know two different points to find the line passing through…

A: Given statement is 'True'

Q: Suppose there is a straight line from z1 = 0 to z2 = 2+4i You know that the equation of a straight…

A: Given, Z1= 0 Z2= 2+4i We have to find the slope(m) of the straight line joining Z1 and Z2

Q: What can you conclude if you know that the point (p, q) lies on the line y = mx + b?

A: We have to conclude if the point p, q lies on the line y=mx+b. We know that if any point is lying on…

Q: 12. For the two non-parallel straight lines L:2x- 5y+ 21 = 0 and L: 3x+y+6 = 0, find the coordinates…

A: Consider the following: Line-1:  2x−5y+21=0Line-2:     3x+y+6=0 At intersection point: L1=L2…

Q: The slope of line I is x, and the slope of line m is x +2. If llm, what is x?

A: Perpendicular lines have slopes that are the opposite of the reciprocal of each other. in given…

Q: The lines joining the origin to the point of intersection of the line lx+my=1 and y²=4ax are at…

A:

Q: Find the distance between the point (2, 9) and the line y = 3x + 4

A: Find the distance between the point (2, 9) and the line y = 3x + 4 To find the distance between a…

Q: What is the distance between the line with Cartesian equation x-4=y-4=z and the line with Cartesian…

A:

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 4?

A: Consider the equation of the parabola, y=ax2 differentiate the equation with respect to x to find…

Q: For what values of a and b is the line 4x+y=b4x+y=b tangent to the curve y=ax3y=ax3 when x=5x=5? a=…

A:

Q: A horizontal line is given by an equation of the form................... ,where b is…

A: We have to fill in the blanks: A horizontal line is given by an equation of the form --, where b is…

Q: find the distance from the point to the line (2, 2, 0); x = -t, y = t, z = -1 + t

A: Given information: The point to the line is (2, 2, 0) and x = -t, y = t, z = -1 + t. Calculation:…

Q: find the distance from the point to the line. (-1, 4, 3); x = 10 + 4t, y = -3, z = 4t

A: Given  Point = P (-1, 4, 3) Equation of line : L1 :  x = 10 + 4t, y = -3, z = 4t Rewrite the…

Q: 45. Parallel to -3x + 4y = 12, passing through (-4, – 6)

A: The line is parallel to -3x+4y=12, passing through -4,-6

Q: What can you conclude if you know that the point (p, q) lies on the line y — тх + b?

A: The given equation of the line is, y=mx+b If a point lies on the line then the point satisfies the…

Q: what is the geometric plàce of points multiplication two given whose of their distance to the lines…

A: Let the line be L1 and L2 having points (x1 ,y1 ) and (x2 ,y2 ) and locus of the geometric place of…

Q: The midpoint of the line segment between P1 (x,y) and P2 (-2,4) is Pm (2,-1). Find the coordinates…

A:

Q: What is the value of d that makes lines e and f parallel?

A:

Q: Find the distance between the point (-1, 3, 5) and the line given by x = 3 + t, y = 1- 2t, and z =…

A:

Q: Two straight lines 3x - 2y + 5 = 0 and 6x - 4y + 10 = 0 A Intersects at the origin B. Are…

A:

Q: Find the distance from the point (2, 2, 3) to the line x = 0, y = 2+ 5t, z = 3+ 3t.

A: