1. A bug crawls on the plane z = 2x +y, from the point (-2, 4, 0) to the point (2, 4, 8) along a path whose projection down on the x-y plane is the parabola y = x? (-2

Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

A:

Q: 2-) Find the Symmetric form of the equation of the line of in tersection of the two Planes X- +Z =2,…

A:

Q: Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what…

A:

Q: 9. Find the equations of the planes that are parallel to 2.x - 2y + z = 5 such that the distance…

A: We will solve the problem.

Q: 2 2. Find an equation of the plane containing the point P(0, -) and the line determined by the two…

A:

Q: 1. Using Euler's equation, show that the shortest distance between two points (r1, yn, z1) and (r2,…

A: Given, the points are (x1, y1, z1)   and  (x2, y2, z2).

Q: 2) The distance between the parallel planes ax + by + cz + d1 = 0 and |d1-d2| ax+by+cz + d2 = 0 is…

A: We find required equations of plane parallel to given plane.

Q: What is the equations of the tangent line in the given plane 1. Tangent to the parabola z = x^2 +…

A: The given surface is:…

Q: 1. Find the distance from the point S(2,-3,4) to the plane x+2y+ 2z =13

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 29 40. A ray of light coming along the line y x + 1 from positive x-direction strikes a concave…

A: Given: A ray of light along the line y=x+1 from positive x-direction A concave mirror whose…

Q: b. Find the distance from the point (2, –2, 3) to the intersection of the planes 2x – y + 3z = 1 and…

A:

Q: (42) is the distance between the point (1, –3, –2) and the plane x- 4y-3z-2= 0.

A: In this question we have to find the distance between point and plane. Note: As per our policy we…

Q: 4. Find a plane through Po(2, 1, –1) and perpendicular to the line of in- tersection of the planes…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: In the xy-plane, how many points on the curve y² + x² = 3 – xy have horizontal or vertical tangent…

A: The given curve is  y2+x2=3-xy

Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: To find the distance from the point 0,1,1 to the line of intersection of the planes:…

Q: 5. Among all the points on the graph of z = 10 – x² – y² that lie above the plane r+2y +3z = 0, find…

A:

Q: 3. Among all the points on the graph of z = 10 – x² – y² above the plane x + 2y + 3z = 0, find the…

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: locus of the circumcentre of variable triangle having sides x = 0 , y = 2 and lx + my = 1 where (l ,…

A: Ans:-             C=0,1m, B=1-2ml,2,A0,2           let h,k be the circumcenter 07 ∆ABC…

Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

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Q: Determine shortest distance of the line 2x-3y-8 to the vertex of the curve x2 - 4a 4y +4 0. O 2 O…

A: We have given a line ,and find the shortest distance from vertex of parabola to line.

Q: A. Show that the planes (x+y- z = 1) and ( 2x - 3y + 4z = 5 ) are neither parallel nor…

A: Let's find.

Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

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

A:

Q: 4. Write the equation of the plane parallel to the z-axis, with xy-trace x + y - 2 = 0.

A: Write the equation of the plane parallel to z axis, with xy trace x+y-2=0.

Q: Among all the points on the graph of z = 10 − x2 − y2 that lie above the plane x+ 2y + 3z= 0, find…

A: We have, z = 10 - x2 - y2 and equation of plane is , x + 2y + 3z = 0 The required point on z = 10 -…

Q: Prove that the curves y2 = 4x and y2-6x+1 = 0 touch each other at the point (1,2)

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Q: Suppose we need to find an equation of the plane that passes through the line of intersection of the…

A: Since, we know that equation of a plane passing through the intersection of planes P and Q is given…

Q: If the line L: X = 3 + 2t , Y= 2t , Z=t intersects the plane X+ 3y Z -4 in a point P. The…

A:

Q: 8) Determine if the line given by r(t) = intersects the xz-plane. If so, determine at what point.

A: we have to find the point of intersection.

Q: Among all the points on the graph of z = 10-x2 -y² that lie above the plane r+2y+3z = 0, ind the…

A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.

Q: 3. Consider the graph of z=r -y". (a) What shape are the traces parallel to the ry-plane? Are there…

A: given z=x2-y2 (A) what shape are the traces parallel to xy plane? are there any restricition on the…

Q: FInd c and d so that the curve y = x3+ cx2+d will have a relative extrema at (2,5). Find other…

A: Given y=x3+cx2+d

Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to…

Q: 2. Find the eanation of the plane Containing the point (2,3,3)'and the line Of intersÉCtion 'of the…

A: We have to find the equation of plane containing the point (2, 3, 3) and the line of intersection of…

Q: Suppose there are two lines in the xy-plane in R^2.  These two lines could intersect at a single…

A: let the lines be                              y=m1x+c1y=m2x+c2 given that lines are intersecting in…

Q: 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two…

A:

Q: 6) = Find the point at which the line intersects the given plane. x =3 - t, y = 2 + t, z = 5t; x - y…

A: Equation of a Line in Parametric Form: where are functions of and is the parameter The equation of…

Q: Find the shortest distance between (3,4,1 ) and the plane X+y +Z = -2

A: Using distance between plane and point formula we can calculate.

Q: The line L(t) = (2+1,8-31, 2t-6) intersects the plane 2y - 3x + 3z = -11 at the point

A: Given, the line             Lt=2+t, 8-3t, 2t-6                                   ...(1) Intersects…

Q: Find the shortest distance from the origin to the line of intersection of the planes 2x + y − z = 1…

A: Given: The planes: 2x+y-z=1 and x-y+z=2.

Q: Show that the curves 2x2 + 3y2 = 5 and y2 = x3 are orthogonal.

A: To show that the two curves are orthogonal.

Q: An equation of a plane P passes through the point (0, 0, 3) and perpendicular to the line L:x =1 –…

A: Remember that the vector (l, m, n) is parallel to the line with parametric equationx=a+lt, y=b+mt,…

Q: 1. Determine the point of intersection of the line and the plane if it exists. π: 7x+y+ 5z = 0 x-4…

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Q: 5. Are there any points on the graph of x2 – y² – 22 = 1 where the tangent plane is parallel to the…

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Q: 1. Let P(x1, Y1) be a point on the parabola x?: be the angle between the parabola and the line…

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Q: A y=1 x=y² B y=x² C (11) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1, and…

A: Given: Three regions A, B and C defined as: where region A is bounded by the parabola x=y2 and the…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.