A hiker realises that the sun is going down and she forgot her headlamp. If the surface of the mountain is represented by z = x²y and the hiker is at a point with coordinates (3, 2, 18), in which direction should the hiker walk to descend the mountain most rapidly?

Q: What will be the axis of symmetry, the line about which a figure or curve is upon itself, between…

A: Given :   y=4x-2

Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

A:

Q: Find the foot of the perpendicular drawn from (4,1) upon the straight line 3x-4y+12=0

A:

Q: In the general form Ax + By + C = 0, can I immediately determine that theslope is A and the…

A: We will write the given equation in the slope-intercept form.

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: H

Q: Solve for the orthogonal traysctories x*(3k-x) - ky². = x ? 2

A:

Q: Find the length of the curve y = x2, 0 ≤ x≤√3/2.

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A:

Q: The point (a,b) and (c,d) are points on the graph of y= x3+5 whose tangent lines are perpendicular…

A: y=x3+5slope at a,b =2x2=2a2     ...(1)slope at c,d =2x2=2c2     ...(2)slope of given line = -13…

Q: Which of the following equations have x-intercepts at (-9,0) and (-3, 0) Ov = (2 - 3) (z - 9) %3D…

A: To find the equations that have x-intercepts at (-9, 0) and (-3, 0)

Q: parallel

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A:

Q: Graph the pair of aquadiope on the Sanme axes, and sfate whe ther they are parallel, porpendieulr,-…

A: Given: 3x-2y=5;6y-9x=6To identify whether it is parallel or perpendicular or neither Clearly the…

Q: The surface of a mountain is modeled by the equation h(x, y) = 7000 - 0.001x2 - 0.004y2. A mountain…

A:

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: / uousənd Solve for x and y in the parallelogram. (3x 4) (4y +'3) X =

A: Solution:- Given the parallelogram                            we need to find the value of x and…

Q: Determine the equation of the perpendicular bisector of KL if it's endpoints are at K O-7,5) and…

A: Given:    Points : K ( 7 , 5 )    ,   L ( 9 , 1 )

Q: Find the coordinates of the other point whose one end is (1,0) and its midpoint is (0,1)? O (1,-2) O…

A: Let's find.

Q: The graph of the curve described by the paramnetric equations x = 3t – 4, y = 6t + 2 is a straight…

A: Consider the curve  x=3t-4,y=6t+2

Q: Find the point(s) of intersection of the parabola y =x2+ 2 andthe line y = x + 4.

A: The given functions are y=x2+2   and   y=x+4

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 5? a = b…

A: Given: The line 4x+y=b is tangent to the parabola y=ax2 when x=5. To Find: Value of a and b.…

Q: find the point p such that v=pq has the components (5,-7,-4)

A: find the point p such that v=pq has the components (5,-7,-4)

Q: Find the point P such that v = PQ has the components (-7.75, –8.25, – 16). О 3D (-2.75, -2.25, -6) P…

A:

Q: ) Eliminate the parameter t to find a Cartesian equation for: x = t² and y = 3 + 5t. and express…

A:

Q: Find the equation of the set of points which are equidistant from (3,10) and the x-axis `y-x -5)²+3…

A: To find the correct option

Q: analyze and trace the given curve y = 2x3 + 3x2 - 12x + 7

A: Given:

Q: Find the slope intercept form of the line satisfying the given conditions. parallel to 4x+16y=23.…

A: The line parallel to the given line 4x+16y=23 should have the same slope as the given line.

Q: Find the veeton equation of a Line L going thagh the P= C-6,2) $ paeallel to the ine point %3D…

A:

Q: Find the real number ( B ) such that the line of symmetric equations ( x - 3 = = ) is parallel to…

A:

Q: Given the points A(3,5) and B( – 3, – 7), find d. the scalar equation of the line.

A:

Q: The equation of the line that goes through the point (1,1) and is perpendicular to the line 4x+4y=4…

A: Given,           The equation of the line that goes through the point (1,1) and is perpendicular to…

Q: Find the foot of the perpendicular drawn from (4, 1) upon the straight line 3x - 4y + 12 = 0.

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A: Definition used-   To keep the temperature constant, the insect has to move in a direction that is…

Q: Find the equation of the normal line to the parabola y=x^2+2x−3, that is also parallel to −2x+2y=9

A: Given that normal line to parabola is parallel to -2x+2y=9. Slope of the line -2x+2y=9 is -…

Q: Find the best quadratic approximation, Q(r, y) of V9 – 6x – 4y for (r, y) (0,0). near

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A: As a first step we need to find the gradient of the surface and evaluate the same for the point (1,…

Q: Given the point P (2, 4, –1) and the line L: x = 1+ t; y=2+ 4t ; = =-3t Find the equation of the…

A:

Q: an object is traveling on a path of y=sprt(x+3) where will the object be closest to (2,0)

A: We have to find the closet point to (2, 0)

Q: Find the point on the parabola x = t, y = t2, -∞ < t < ∞ closest to the point (2, 1/2).

A: Given Data The first equation is x=t. The second equation is y=t². The point is (2,1/2).…

Q: What are the lengths of the major and minor axes of 16r + 49y - 32x + 294y – 327 = 0?

A:

Q: Find an equation of the normal line to the parabola y = x2 - 8x + 9 that is parallel to the line x -…

A:

Q: Find the equation of the curve for which y" = x, and which passes through the point (1, 2) with (A…

A: Given y'' = x  and the curve passes through (1,2)  with a slope of 5/2. which means y(1) =2, y'(1)…

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

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: Solve for the orthogonal traectories y = x2- cX

A: The orthogonal trajectory is a curve that intersects each of the family's curves at a right angle.…

Q: (A) Find the unique point P on the y-axis which is on both planes. (–, ,

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: A point moves so that the ratio of its distances from 3x + 4y + 8 = 0 and 4x + 3y – 6 = 0 is 2. Find…

A:

Q: Find the values of x and y in parallelogram PQRS. PT = y, TR = 4x + 1, QT = 2y, TS = 3x + 12 and y =

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A:

Q: Find the equations of the line through (2,0, –4) and parallel to each of the planes x + y – z = 0…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.