2) Consider the curve defined by -8x² + 5xy + y³ = -149 dy a) Find dx b) Write an equation for the line tangent to the curve at the point (4,-1).

Q: the sloper of the curve 2y2=ax2+b at (1,-1) is -1.Find a,b

A: 1) Find dydx at the given points to find the value of 'a' . 2) Now satisfy the point (1,-1) to the…

Q: Determine a, b, c and d so that the curve y = ax³ + bx² + cx+d₂ pass through (-1, -1) and have at…

A: To Determine: Value of a, b, c and d so that curve y = a x3 + b x2 + cx + d

Q: Find the equation of the line tangent to the curve xy^3+xy=6 at the point (3,1). When the equation…

A: Firstly, we will find derivative And then we can solve for y'and we get

Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

Q: Find the tangent plane to the equation 5e*- öy at the point (12, 24, 5).

A:

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: Show that there is a line that is simultaneously tangent to both the curves y = ex and y = lnx.

A:

Q: The equation of tangent to the curve y =x- at (1,- 2) is-- O a. 13 y +1 = (x– 1) O b. 25 y - 2 = (x…

A:

Q: Please help me find the length of the curve

A: We\'ll use arc length formula with a=pi/2, b=2pi/3.

Q: How many horizontal tangent lines does the curve parametrized by the equations z(t) =-4t-1,…

A: on doing derivative we get the 1

Q: What is the equation of line L passing through (-1,3) that is tangent to the curve…

A: Let's Solve, Answer : Option E

Q: Consider the curve defined by the equation y3+xy+2=0.  Show that there are no points on this curve…

A: Consider the given curve define by the equation:

Q: Consider the curve defined by the equation y³ + xy + 2 = 0. Show that there are no points on this…

A: Given Equation of curve   y3+xy+2=0  ---(1)

Q: The Slope of the tangent line to the at the point C7,3) is: Curve y=

A:

Q: find equation for the lines that are tangent andnormal to the curve at the given point. ex + y2 = 2,…

A: Given: Equation of curve ex+y2=2 and the point 0,1, To find: Equation of tangent and normal line to…

Q: The equation for the tangent line to the curve y=x3 which passes through the point (0,2) is y=mx+b…

A:

Q: Find the equation of the tangent line to the curve y = x+5x* which is passing through point (1, 3):*…

A: Given : Curve  y = x + 5x2 Point 1,3   To find : The equation of the tangent line to the given…

Q: Find the tangent plane to the equation 4x2 + 3y2 – y at the point (-4,-1,68) Z =

A:

Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point (6,0)? A y = x -…

A: Given, The equation of the curve ey+cosx = 1 We have to find the equation of the line tangent at the…

Q: What point on the curve y = Vx is closest to the point (5, 0)?

A: Use distance formula between two point and then differentiate

Q: Find the coordinates of the points on the curve y= x' + 5x + 3 at which the tangent: makes an angle…

A:

Q: The equation of tangent line to y =27 7sinx at the point () is is: Select one: a. y=2x b.y=-2x+2T O…

A:

Q: Find the equation of the tangent line at the given point on the curve. 2y- Vx 28, (16,4) y=D

A: 2y2-x=28,    16, 4. Slope of the tangent line is the derivative of the given function at the given…

Q: d two coordinate points at which the tangent line to the curve given by x² – 2x + 4y² = 15 is…

A: if the tangent is vertical then dydx will be ∞x2-2x+4y2=15differentiate 2x-2+8ydydx=04ydydx=1-xsince…

Q: The slope of the tangent line to the parabola y 4x + 7x + 5 at the point (0, 5) is: The equation of…

A:

Q: #1 Find the equation of the tangent line to y:R @ x- -4 Provide answer in point-slope form dy %3D

A: Differentiate at given point then use equation of line

Q: Find the equation of the line that is tangent to the curve r = x In y, x > 0, at the point (1,е).

A: Equation if the line (y - y1) = m(x -x1) D(uv) = uDv + vDu , where D is the differentiation of…

Q: What is the slope of the tangent line to a curve with parametric equations of x= 2t+1 and y= 3t-1? *

A:

Q: d the equatiom of the tangent line to the curve xy – 7 = Vx + y² at the point (5,2).

A: For finding tangent line to the curve , find the derivative of the function and put the value of…

Q: At what point is the tangent line to the curve y = 2x perpendicular to the line x – - 2y – 8 = 0? -…

A:

Q: Make the curve y=ax³ +bx²+cx+d pass though (0,3) and have at (1,2) a point of inflection with a…

A: Given: T curve y=ax3+bx2+cx+d passes through the point (0, 3). The point of inflection is (1, 2)…

Q: 12. What is the equation of the tangent line to the curve y = x² – 2x + 1 at point (3,4)? a. у%3D 2х…

A: Since the student has mentioned to solve question numbers (12) and (13), but we can solve only one…

Q: The equation of the tangent line to the curve x² + y² = 64, at (9,-14) is

A:

Q: An equation of the tangent line to the curve y= cos(x) at a = T/3 is (- 7/3). %3D y =

A:

Q: At what point is the tangent line to the curve y = 6x² perpendicular to the line x + 2y – 8 = 0?…

A: Follow next step

Q: Find the equations of the tangent lines x = 2 sin 2t, y = 3 sin t at the point where the curve…

A: Consider the given equation as x=2sin2t, y=3sint

Q: Find the second derivative of the parametric equation = 9t2 + 4 , y=3(t − 2)2

A:

Q: The equation of the tangent line to the curve x? + y² = 64, at (5,-18) is

A: The given equation is x2+y2=64 Differentiate both sides w.r.t. x, 2x+2ydydx=0 dydx=-xy evaluate dydx…

Q: At what point is the tangent line to the curve y° = 6x² perpendicular to the line 2x – y – 1 = 0?…

A: Given: y3=6x2..(1)2x-y-1=0y=2x-1...2   As we know that, iI two lines are perpendicular to each other…

Q: Find the equation of a line normal to the curve x^2=16y at (4,2).

A: Solve the given problem.

Q: Find the slope of the line tangent to y = 3x(cos x) at (7/2, 7/2). A) -3/2 B) 3x/2 C) /2 D) -x/2

A: Consider the function  y=3x(cosx) Point : π2,π2

Q: Show that the line y = mx + b is its own tangent line at any point (x0, mx0 + b).

A: Given:Show that the line y = mx + b is its own tangent line at any point (x0, mx0 + b).

Q: The slope of the tangent to the curve y²x + y²a² = 6 at (2, 1) is A B) -1 в 14

A: We can find the slope of the tangent to the curve at the indicated point as below.

Q: Find the equation of the line tangent to the curve xy3+xy=20 at the point (10,1). When the equation…

A: It is given that, the equation of the curve is xy3 + xy  = 20. Use implicit differentiation to…

Q: Find the equations of the lines tangent and normal to the curve guen by para- metric equations at +…

A:

Q: Find the equation of the tangent line to the curve y = e' when it is paralel to 2r-y =7.

A:

Q: 4) Find the equation of tangent I point line to the circle below at point (1,-3). * x² + y² – 2x –…

A: Consider the given equation of the circle, x2+y2-2x-4y-20=0 The equation of the tangent line passing…

Q: The curve defined by the equation x^2+y^2=(2x^2+2y^2-x)^2 is called a cardioid. Find the equation of…

A: consider the given equation, x2+y2=2x2+2y2-x2 Use implicit differentiation method and differentiate…

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.