2. Find the shortest distance from the point (2,0) to the curve: (a) y = 3x – 1 (b) y = x^2 (c) x^2 + y^2 = 1

Q: Make the curve y=ax*+bx³+ cx²+ dx+e pass through the points (0,3) and (-2,7) and at (1,4) have a…

A:

Q: Find the length of the curve x = 49 sec* t – 1 dt with 3 - - 6. Length is

A:

Q: Find the ordinate of the center of curvature of the curve y² = 4x at point (2, 4) from the x-axis.

A: Given option are wrong, option c should be '-16'.

Q: Find length of curve: y=3x^(3/2) from x=0 to x=4

A:

Q: 25 at the point ( 1, -1, 2 ).

A: Given that : The surface  8x2+y2+4z2 = 25 , point = ( 1, -1, 2 ).

Q: 4. Find the point on the curve y = 2x² – 12x + 5 where the tangent is horizontal.

A:

Q: 5. What is the maximum vertical distance between the line y = x + 2 and the parabola y = x² for – 1…

A: The given equations are, y = x + 2       ....(1)  y = x2            ....(2) To find the maximum…

Q: Find an equation of tangent equation is 2x+6y=3. line to the graph of y=x+lax that is perpendicular…

A: We need to find the equation of the tangent line to the graph y=x+ln(x) that is perpendicular to the…

Q: Find the length of the curve y x² Inx 8 at (2 <x< 4)? -

A:

Q: 6. Find the equation of the tangent plane to the surface: ==√√4-x²-2y², at (1,-1, 1)

A:

Q: What is the maximum vertical distance between the line y = x + 51 and the parabola y= x² over the…

A: Given: The line y=x+51 and the parabola y=x2 To find: Maximum vertical distance between given line…

Q: Find the ponits on the curve 9y2 =x3 where normal to the curve makes equal intercepts with axes

A:

Q: The Normal to the curve 2x² – y² = 1 at the point (1,1)

A:

Q: find the point on the line y=2x+10 that is closest to the orgin, (0,0) What is the minimum distance?

A:

Q: Determine the coefficients a, b, c, d that will make the curve y = ax3 + bx2 + cx +d passes through…

A: Given y=ax3+bx2+cx+d

Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for −1 ≤ x…

A: Consider the given line

Q: Find the maximum area of a triangle formed by the axes and a tangent line to the graph of y = (x +…

A: Find the maximum area of a triangle formed by the axes and a tangent line to the graph of y = (x +…

Q: Find the equation of the tangent line to the common curve of the two surfaces with equations z = x²…

A: Please check step 2 for solution.

Q: Find the points on the curve y = 2x' + 3x² – 12x + 1 where the tangent is horizontal. -

A: As per the instruction, we will be answering the first question. For (51), Given: y=2x3+3x2-12x+1.…

Q: Find point on the ellipse x^2+2y^2=1  where the tangent line has a slope of 1.

A: We know, slope of tangent line = dydx

Q: Find the point (xo, Yo) on the graph of y = x³ + 3x² + 5x – 3, at which the slope of the tangent…

A:

Q: Find the exact length of the curve. 1 y = 1 + cosh(8x), 0 ≤ x ≤ 1 8

A:

Q: Find the equation of the circle of curvature of the curve y = 2x" – x at its minimum point in the…

A: The equation of a circle is defined using the formula: x-h2+y-k2=r2, where h, k is the center and r…

Q: Find the equation for the tangent plane to the surface x2 - 5xyz + y² = 7z2 at the point (-1, -1,…

A: Simplify the given equation of the surface in the form F(x,y,z)=0. x2-5xyz+y2=7z2x2-5xyz+y2-7z2=0…

Q: 4. Find the radius and center of curvature of the curve y=6x-x³ at the point (1,5).

A: This question is based on radius and centre of curvature formula.

Q: Find the ponits on the curve 9y2=x3 where normal to the curve makes equal intercepts with axes

A:

Q: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: 6. Find the equation of the tangent line to the parabola y 2.x2 – x + 3 at x = 2. %3D -

A: Equation of given parabola is, y = 2x2 - x + 3

Q: find the length of the curve 3y2=4x3 from x=0 to x=8 when y greater than or equal to 0.

A: The formula for length of a curve f(x) extending from point a to point b is given as,

Q: What is the equation of the line tangent to curve defined by x + 4y² = 17 at the point (1, -2)?…

A: equation of line tangent

Q: find the slope of the tangent to the curve of intersection of the surface 3z=√36-9x²-4y² and the…

A: Consider the surface 3z=36-9x2-4y2and the plane x=1 at the point 1,-2,113.The objective is to find…

Q: 2. Find the coordinates of the points on the curve y = r' - x² – x +1 where the tangent line is…

A: Solution:- step-by-step solution of above  question is given below.. The given curve is  y=x3-x2-x+1…

Q: Find the slope of the tangent to the curve r+ 2xy + y = 16 at (1, 3). The slope is VEnter undof if…

A:

Q: Make the curve y=ax²+bx+ c pass through (2,1) and be tangent to the line y=2x+4 at (1,6)

A:

Q: What is the moment of inertia about the x-axis bounded by the curves y² = -16(x-4), the line 8x-15y…

A: here we have to find the moment of inertia about x axis so we can use integration to find this.

Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

Q: How can we find the slope of the tangent line to the parabola y = x2 at the point?

A: Consider the following equation of parabola: y=x2 Differentiate y with respect to x: dydx=ddxx2=2x

Q: Find equations of the tangent and normal line to the curve y (2x+1) %3D at x=2. (3x2-2)

A:

Q: Find the point on the curve y = x³ + x2 – 1 where the tangent is perpendicular to the line y = -x

A:

Q: Find the length of the curve for 12x = 4y³ + 3y-¹ where 1 ≤ y ≤ 3 Enter your answer in exact form.…

A:

Q: Show that the tangent line to the curve at y = 3x²+ 6x− 5 the point (−1. −8) is horizontal.

A: To show: That the tangent line to the curve at y=3x2+6x−5 the point -1,-8 is horizontal. Concept…

Q: Find the equation of the tangent line to the common curve of the two surfaces with equations z = x²…

A: Please check step 2 for solution.!

Q: What is the average distance between the parabola y = 7x(16-x) and the x-axis on the interval…

A:

Q: Consider the curve satisfying y" = 6x and is tangent to the line y = 5– 3x at x = 1. What is y' (2)?…

A: Given: y''=6xand tangent to the line y=5-3x at x=1To find y'(2)=?

Q: Find the equation of the tangent plane and the normal line to the surface x +y = 6xyz +8z2 at the…

A:

Q: Find the slope of the tangent to the curve of intersection of the survace 3z =√36 – 9x² – 4y² and…

A:

Q: find the slope of the tangent to the curve of intersection between 6z=3squareroot(20-x^2) and the…

A: the cylinder equation is given by  and the plane is given by  We want to define each variable in…

Q: What is the maximum vertical distance between the line y = x + 29 and the parabola y = x² over the…

A:

Q: What is the maximum vertical distance between the line y = x + 38 and the parabola y = interval [–…

A: Given line equation is y=x+38 Given parabola equation is y=x2 From the above two equations x2-x-38=0…