Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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: Find the max. and min. values of (x, y) = x² – xy + y on the quarter circle x² +y =1 where x.y20.

A: I use langrange multiplier method

Q: Find the point (a, b) on the graph of y = ex where the value ab is theleast.

A:

Q: Find the points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the three coordinate planes.

A: Given line is  x = 1 + 2t, y =-1 - t, z = 3tWhen the line meets xy plane then z=0So, 3t=0Or, t=0

Q: Find the equation in the xy-plane whose graph includes x In(6t) and y = t².

A: Given  x= ln(6t) y=t2

Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: Sz(t) = - 2t2 ly(t)…

A: The objective is to to eliminate the parameter t to find a cartesian equation

Q: Find the point on the plane x + 2y + 3z = 13 closest to the point (1, 1, 1).

A: Given plane is We need to find the point on the plane closest to

Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

Q: Find the trace of the plane 8x – 9y + 2z = -11 in the coordinate xz-plane.

A:

Q: F· dr, where F(x,y) = –lj, and C is the part of the graph of y = - x from (2,2) to (–2, C

A:

Q: Find a plane containing the point (6, -4,-3) and the line (t) = +t 270

A:

Q: Sketch a graph of I = t + 2t, y = t +2, t > –1 . %3D

A: Given equations are x=t2+2t,y=t+2,t≥-1. So list the values of t and obtain the coordinates in…

Q: 1 2x 3y + z = 0 and 2 +t - 1 1

A:

Q: find the trace of the plane in the given coordinate plane.  −x + y = 4, xz

A: Find trace of the plane in the coordinate plane -x+y=4 in xz

Q: Find the​ distance, d, between the point S(6,9,10) and the plane 10x+7y+1z=60.

A: Answer is 73/5√6.

Q: Determine the type of the following equation and reduce it into it's canonical form: - y zyy = ry,…

A: The second order semi linear partial differential equation can be classified as…

Q: Find the equation of the plane containing the point P(1, 1, –1) and the line -4+t 1- t 1+t

A:

Q: Find the trace of the plane in the given coordinate plane.3x − 9y + 4z = 5,  xz

A: Let the plane P whose equation is:                                          3x-9y+4z=5…

Q: Find the orthogonal trajectory of the circles x² + y² + ay = 0

A: GIvenx2+y2+ay=0To findorthogonal trajectory of above curve.

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: Find all hyperbolic lines that passes through i +1 and parallel to the y-axis.

A: Find all hyperbolic lines that passes through i+1 and parallelto the y-axis.

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Consider the given equation as x=t3....(1) And y=t2....(2)

Q: Find the coordinates of the reflection without using the coordinate plane. Q(-3,5) over the y-axis.

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: If 1x, y2 are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

A: If (x,y) are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Find the equation in terms of x by substituting x=t in the given expression   y=t2-1=x2-1   To use…

Q: Describe with a sketch the sets of points 1x, y, z2 satisfying the following equations. y - z = 0

A: First sketch the graph of the function y-z=0 as shown below.

Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: Find a plane containing the point (-3,3,-3) and the line F(t) = +t

A:

Q: Find the point on the plane x+ 2y - z 12 that is nearest the origin.

A:

Q: Graph the first-octant portion of each plane. x + y + z = 15

A: Given a Plane, x+y+z=15 We need to graph the above plane.

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

A:

Q: Find the condition for the points (a,0) ,(h,k),(0,b) when ab is not equal to 0 to be collinear

A:

Q: Find the trace of the plane in the given coordinate plane. Зх — 9у + 82 %3D7, yz

A:

Q: 5. Identify and sketch the graph of the following equations in R³. (a) a2 + 4y? + 22 – 8x + 16y – 2z…

A:

Q: find the equation of the secant lines of y=√x passing through the points: x1=1 and x2=2

A: Secant line for a function between two points on a curve is simply a straight line passing through…

Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…

Q: Find the point at which the line 7(t) = +t intersects the yz plane.

A:

Q: Find the condition for the points(a, 0).(h, k)(0, b) when ab 0 to be collinear.

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

Q: Find an equation for the set of points equidistant from the y-axis and the plane z = 6.

A: we  have to find an  equation for the set of points equidistant from the y-axis and the plane z =…

Q: find the equation of the line through (0,2,1) that is perpendicular to both u= 4i + 3j − 5k and the…

A:

Q: Find the exac length of the curve 3/2 , 0dxE y=2+2x

A:

Q: (c) Given that y = x4 – 8x²

A:

Q: Find the point at which the line 7(t) +t intersects the | xz plane.

A:

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: trace the path of the curve f(t) = (3e', 4e24)

A:

Q: If C1 is the segment connecting (x1, Y1) to (x2, Y2), find | x dy – y dx in terms of the four…

A:

Q: Find the points PCo10,0),Q Ce,2,0) and RCOl- thal- 2I to the line: the Line in the Plane of passes…

A:

Q: Find the relationship between x and y such that the point (x.y is equidistant from the point (7,1)…

A: If a point say P is equidistant form two points say A and B then  PA =PB To see complete solution…

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.