4) Let P = (x,y) be a point on the graph of y = x² – 8. a) Express the distance d from P to the point (0, –1) as a function of x. b) What is d if x = 0? c) What is d if x = -1?

Q: 5. Show that the equation of the tangent to the curve y = Inx + kx at x = 1 always passes through…

A:

Q: (a) Find all the points on the graph of (x² + y? + y)2 x² + y? that have horizontal tangent line.

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

Q: Please show step-by-step solution!

A:

Q: The slope of the tangent line to the graph of f(x) D x2 at a = -1 is: %3D %3D

A: Given  equation of the graph  f(x) = xx2-x                        ...........(1) We have to find the…

Q: what is the largest vertical distance between the graphs of the functions y=x^1/2 and y=x^2 in the…

A: To find the largest vertical distance between the graphs in the interval given

Q: Find the x Coordinate of the point on the graph of 4=x² where the to the Secant. Longent tine.…

A:

Q: Prove that the curves y=f(x),(f(x)>0) and y = f (x)sin x, where f(x) is differentiability function,…

A:

Q: Find the slope of the tangent line to the curve of intersection of graph of f and the plane x =2 at…

A:

Q: Find the length of the following curve. y = 2x + 4 on 3-2, 24 (Use calculus.)

A:

Q: Assume every secant line of the curve y = f(x) has slope at least 3. Then every tangent line of the…

A: Given: Every secant line of the curve y=fx has a slope atleast 3.Then every tangent line of the…

Q: 9. What is the equation of the line tangent to the graph of the function f at the point (1,1)? f (x)…

A:

Q: Does the graph of Sx²sin (1/x), x ± 0 f(x) = lo, x = 0 have a tangent line at the origin? Give…

A:

Q: Find all the points on the graph of (x² + y²)² = x² – y² that have horizontal tangent line.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 3. What is the equation of the tangent line to the curve x3 + x² = y which is parallel to the line…

A: Given the equation of the curve y=x3+x2 and the tangent line is parallel to 3y+x-5=0

Q: Find the equation of the tangent line to the function f(x) = -3x2 – 2x at the point where x form y =…

A:

Q: Prove that the tangent lines to the curves 5y – 2x +y³ – x²y = 0 and 2y + 5x +x* – x³y2 = 0…

A: Given: - The statement is, The tangent lines to the curves 5y-2x+y3-x2y=0and 2y+5x+x4-x3y2=0…

Q: The tangent of the curve x^2+y^2--7 * 2xy3DO at the point (1,1), is a. y-2-х. О b. y=x-2. O С.…

A:

Q: For what values of x in [0,2pi] does the graph of f(x)= x + 2sin(x) have a horizontal tangent?

A: Horizontal tangent:The slope of a tangent of the graph of a function f (x) is df (x) ∕dx. For a…

Q: Find the equation of the tangent plane to the graph of 9y f(x, y) = at the point (4, –-1). (Use…

A: The Equation of the tangent plane: - z0=(x0,y0) is a point in the domain of f, and defined by a…

Q: The equation of the tangent plane of the graph of function z = xy + 2x² - y3 at point (2, -1) is

A:

Q: Find all points on the graph of 3x 2 + 4 y 2 + 3xy = 24 where the tangent line is horizontal

A: Given:              3x2+4y2+3xy=24 We know the tangent line is horizontal when y'=0 So we want to…

Q: at what point is the tangent line y3=2x2 perpendicular to the line x-y-1=0? P=(?,?)

A:

Q: Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y-2y³ In the…

A:

Q: A curve passing through (1, 0) is such that the ratio of the square of the intercept cut by any…

A: We have to find the possible curves that satisfies the given condition.

Q: 2. Let f(x) tan (2) at the point (1, 7)? tan (r). What is an equation to the tangent line to y

A:

Q: calculate the are between the curves f(x)=x^2 and g(x)=x^3 on the interval [-1,1]

A: Given,

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: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1).

A: To Determine: FInd the equation of tangent plane to the graph of…

Q: Find the point (s) on x = 3 - y2 that are closest to point A = (1,0).

A: Given: x = 3 - y2 and point A = (1, 0)

Q: Find the length of the curve y = In (1 – 2*) over the interval [-,].

A:

Q: Prove that there no line through the point (0,1) is tangent to the graph of y = x*.

A:

Q: Use four equal-length Hermite curves to interpolate y = sin(x) in the interval [0,2π].

A: To interpolate y = sin(x) in the interval [0,2π] using four equal-length Hermite curves

Q: 1. Use four equal-length Hermite curves to interpolate y = sin(x) in the interval [0, 2r].

A:

Q: What is the largest vertical distance between the graphs of the functions y=√x and y=x 2 in the…

A:

Q: find a point c satisfying the conclusion of the MVT for the given function and interval. Then draw…

A:

Q: How many tangent lines to the curve y = x/(x + 1) pass through the point (1, 2)? At which points do…

A: The tangent lines to the curve y=xx+1 passes through the point (1, 2)

Q: Find the equation in terms of x and y of the tangent line to the curve r= 4sin 5θ and θ =π/3.

A: Given: r=4sin5θ  and θ=π3

Q: Find the exact value of x in the given interval that has the given circular function value.

A:

Q: The point on the graph of f(x) = 1 where the tangent line is parallel to the line 3z + y = 1 is: %3D

A:

Q: The tangent line to y=f(x) at (1,-3) passes through the point (3,9). Compute the following: f(1)=?…

A:

Q: What is the image of the horizontal line through the point in under e ?

A:

Q: Show that th equation of the tangent to the curve X 1승 +1-2(a 0,b + 0) at the point (a,.b) is 즈+-2 X…

A:

Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

A:

Q: Find the equation of the tangent plane to the graph of f(x, y) = In (13x² 10y²) %3D at the point (1,…

A: Solution is written in below steps.

Q: 2 Consider the curve given by f(x)=x²³x + 5 find the equation to the tanget to the curve at point…

A: We know that a line which touches the curve fx at one and only one point is called a tangent line.…

Q: The slope of the tangent line to the graph of xy = In(x² + y² ) at the point (1,0) is :Select one…

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.