11) Find the distance between point A(-3, 1,1) and the line of symmetric equations x = -y = -z.

Q: The equation of the area of the plane region bounded by y = x^3 and the lines x = 1 and y =0 is…

A: Detail solution written below

Q: What are the coordinates of the points in the graph of y² –x²+ 6x – 13=0 in which the tangent line…

A:

Q: Find parametric and symmetric equations for the line satisfying the given conditions. Through the…

A:

Q: What are the equation of line passing through (-1,3) that is tangent to the curve x^2 + 4y^2 – 4x –…

A:

Q: What is the distance between the line with Cartesian equation x-6 = y-1 =z and the line with…

A: Answer

Q: 5. Find the equations of the tangent line and normal line to the parabola y = 2x² at the point…

A: Since, you have asked multiple questions , according to our guidelines we are supposed to answer…

Q: Find distance between point A(1,3) Perpenclicular on the line L: 2y =2 +X

A: Use the following formula: The perpendicular distance from the point A(x1,y1) to the line ax+by+c=0…

Q: 5 Find the equations to both lines through the point (2,-2) that are tangent to the parabola y = x²…

A:

Q: Find equations for two lines through the origin that are tang net to the curve x²-4x+y²+3=0 .

A: We have given equation of curve x2-4x+y2+3=0. We also know that the slope of the line will be the…

Q: Solve the center qnd radius of the circle passing through the points P(1,1) and is tangent to the…

A:

Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, - 1, 2) is parallel | to the line x=…

A: Given that points are (2,1,-1), (0,-2,0) and (1,-1,2) The parametric equation is,…

Q: 16- Find the equation of the plane that contains the line = 2+ = 5-z, and the point P(0,5,2).

A:

Q: Find the distance from the point Q to the line ℓ.

A: Given: Q=0, 1, 0, l with equation xyz=111+t-203.

Q: 8. Determine the equation of the plane tangent to z point (x, у, z) 3 (-2, 1, 4). x*y3 at the =

A:

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A: The symmetric equations of line are given by (x-xo)a = (y-yo)b = (z-zo)cwhere (x0, y0, z0) is a…

Q: Find equations of both lines through the point (5, –6) that are tangent to the parabola y = x2 – 3x

A: topic - equation of tangent to curve

Q: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

A:

Q: Find the distance from point P(2, 7, -6) to the plane of equation 5x - y + 4z - 8 = 0

A: We have to find distance

Q: 7. Find the distance between the point (- 3, 2, 1) and the plane with equation x - 2y + 3z = 5

A:

Q: ) Find the equation of the line normal to the curve x'y+ y'x = 10 at point (1,2).

A: Slope of a normal to the function y=f(x) at point m,n is given by the value of -dxdy at m,n Equation…

Q: Compute x²z ds where Cis the line segment from (0,6,–1) to (4,1,5).

A:

Q: Find the point (s) on x = 3 - y2 that are closest to point A = (1,0).

A: Given: x = 3 - y2 and point A = (1, 0)

Q: The plane through the points (2, 1, –1), (0, –2, 0), and (1, – 1, 2) is parallel to the line x=1-t,…

A: Equation of plane passing through x1, y1, x2, y2, x3, y3 is given by,…

Q: an equation for line L in point-s erpendicular to y 5x. 6Ty=5x (1,5) 2- -4 -2 4 6 2.

A: We will solve the problem

Q: 17. Passes through the point (2, 1) and is perpendicular to y = -x+ 3.

A:

Q: Find an equation of the line through the point (1, 2) that is perpendicular to th = --x +3 Select…

A: The given question is solved below.

Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it using…

A:

Q: What is the length of the curve y3/2+4 from the point (1,5) to (4,12)?

A: To find: The length of the curve y3/2+4 from the point (1,5) to (4,12).

Q: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

A: To find the points at which tangent line is horizontal , y' =0.

Q: Show that the solution of the equation YUx – xUy = 0 containing the curve x² + y² = a², u= y, does…

A: Given that y ux – x uy = 0, The Lagrange’s auxiliary equation for the given equation is given as:…

Q: What is the distance between the line with Cartesian equation x-1 = y-6 = z and the line with…

A: Given:- The line with cartesian equation x-1=y-6=z and the line with the cartesian equation…

Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13= 0 in which the tangent…

A:

Q: Find the distance between point (5,-1) and line x=3y-12.

A: Given: The point (5, -1) and the line  x = 3y -12. To find: The distance between the given point and…

Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A:

Q: What are the coordinates of the points in the graph of y – z² + 6z – 13 = 0 in which the tangent…

A:

Q: Calculate the distance between the points M=(-9,8) and L=(-1, 1) in the coordinate plane. Give an…

A:

Q: 16- Find the equation of the plane that contains the line = 5 - z, and the %3D point P( 0,5,2).

A:

Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

A: As we know that; The slope of the horizontal tangent line is zero or m=dydxPx0,y0=0 Given;…

Q: What are the coordinates of the points in the graph of y-x+6x – 13=0 in which the tangent line is…

A:

Q: 12. Find the distance between the point (3,-2,7) and the plane 4x – 6 y + z = 5.

A: The equation of plane is 4x-6y+z=5 and the given point is 3,-2,7. The distance between the point and…

Q: 2. Obtain an equation for a plane a that includes straight line(2--5) and 1: point(-2,1,1)

A:

Q: slope of the tangent to the curve y2x+ y2x2 =6at (2,1) is

A:

Q: Find the distance between the line x + y + 2 = 0 and the point (1, 1).

A: The distance between the line ax+by+c=0 and the point x1,y1 is given as below. d=ax1+by1+ca2+b2

Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, -1, 2) is parallel to the line x 1-t,…

A: equation of plane for non collinear points , x-x1y-y1z-z1x2-x1y2-y1z2-z1x3-x1y3-y1z3-z1 we will use…

Q: The y-axis and the line x = c are the banks of a river whose current has uniform speed a in the…

A:

Q: Find an equation of the plane tangent and an equation of the line normal to the surface 7z = 4x² -…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Find the equations of the tangent lines to the circle x2 + y2 = 1 which pass through the point (-4,…

A:

Q: 4. Find the member of the curve whose slope at any point is 4y point (3, 4) and passes through the

A: Note: As they are different questions, as per our company guidelines we are supposed to answer the…

Q: ) Find an equation of the tangent plane to the paraboloid defined by -- 4x² + 5y² at the point (,-2,…

A: