Find equations for the tangent line and the normal line to the graph of the equation at the given point. (The normal line at a point is perpendicular to the tangent line at the point.) Use a graphing utility to graph the equation, the tangent line, and the normal line.                                                                 x2 + y2 = 10,         (3, 1)

Q: Find ​the slope of the curve at the given point​ P and an equation of the tangent line at P.…

A: solution:-y=-3-4x2point, P(x1, y1)=-3, -39slope=dydx=ddx-3-4x2=-8xat point -3, -39slope=-8(-3)=24

Q: Find the equations of all lines through the origin that are tangent to the curve y = x - 10x2 – 4x.…

A: Given curve is y=x3-10x2-4x

Q: Find an equation for the tangent line to the curve at the given point. Then sketch the curve and the…

A: The given curve is  y = 2x3 The given point  (2, 16)

Q: Find the equation of the tangent line at the given point on the following curve. 2+y? = 34, (5,3)…

A: For the given curve  x2+y2= 34  And point (5,3)  equation of the tangent line to the point is…

Q: (a) Find the slope m of the tangent to the curve y = 1 + 4x2 – 2x³ at the point where x = a m = (b)…

A: Given equation of curve is: y=1+4x2-2x3

Q: Find an equation of the tangent line to y = f(x) when r = 2. The slope of the tangent line is f'(2)…

A:

Q: a. Find an equation for the line that is tangent to the curve y = x3 - x at the point (-1, 0). b.…

A: (a) Consider the provided equation of curve and point where the tangent drawn is shown below,

Q: Find the equation of the normal line to the given curve at the specified point. (Hint: The normal…

A:

Q: Find equations of the tangent line and normal line to the curve at the given point. y = x4 + 9ex,…

A:

Q: Find the equation of the tangent line at the given point on the following curve x* +y° = 8. (– 2,2)…

A: The equation of of tangent to a curve f(x,y)=0 at a,b is (y-b)=dydx(a,b)(x-a)

Q: Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the…

A: We have to find an equation of the tangent line to the curve at the given point.…

Q: Find the equation of the tangent line at the given point on the following curve. 2. x+y 8, (-2,2)…

A:

Q: A curve is given by the equation x4 + y = 82. Find the equation of the line tangent the curve at…

A:

Q: Find the equation of the tangent line at the given point on the following curve. x? +y? = 17, (1, -…

A:

Q: Find the equation of the tangent line at the given point on the curve. x²y? = 49, (- 1,7) The…

A: Consider the given equation: x2y2=49y2=49x2y=7x Differentiate the Equation: dydx=-7x2 Hence, slope…

Q: Find the equation of the line tangent to the graph of x³ + y³ = − 3xy - 80 at (-4,-4). The equation…

A:

Q: Find an equation for the line tangent to the curve y at the point (4,27). = 3 x - 2 Find an equation…

A:

Q: 7) f) = Sx + 12x -7x at a point where x -1

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Find the equation of the line nomal to the curve y = 3x"-5x at the point (1,-2). Sketch the curve…

A:

Q: Find the equation of the tangent line at the given point on the following curve. x2+y? = 20, (-2,4)…

A:

Q: 5.) y3 x+ at a point where x 3

A: A detailed solution is given below

Q: Find slope-intercept equations of the tangent lines to the graphs of the fo points: (a) flx) (h) Ax3

A: The given function is  a) f(x)=x2-5x+2, at x=-1  b) f(x)=4x3-7x2, at x=3

Q: a. Determine an equation of the tangent line and the normal line at the given point on the curve. b.…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: The slope of the tangent line at any point (x, y) on a curve is 2vx. If the point (9,3) is on the…

A:

Q: Find the slope of the tangent line to the graph of the given function at the given value of x. 3/2…

A:

Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the…

A:

Q: Find equations of the tangent line and normal line

A:

Q: 9.) f@)= 3x 2x + 4 at a point where x 0 10.) fx) = (x + 1)' at a point where x = 1

A:

Q: Find equations for the tangent line and the normal line to che graph x² + y? = 5, (2, 1) tangent…

A:

Q: following

A:

Q: Find the equation of the tangent line at the given point on the following curve. *+y² =41, (-4. - 5)…

A:

Q: Find an equation for the line that is tangent to the caurve y= 3x-3x at the point (-1,0). The…

A:

Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the…

A:

Q: Find y′ and the slope of the tangent line to the graph of the equation below at the indicated point.…

A: It is slope of tangent line.

Q: 15 points) Find the equation of the tangent line to the graph ofx2−4xy−3 = 0 at (1,−12)

A:

Q: The slope of the tangent line at any point (x, y) on a curve is 2vx. If the point (9.3) is on the…

A:

Q: Find the slope of the given point of the equation of the tangent line y=x^2-5 P(2,-1)

A: Slope of the tangent is obtained by dy/dx

Q: Find the equations of the tangent line and normal line to the given curve at the specified point.

A: Find the equations of the tangent line and normal line to the given curve at the specified point. y=…

Q: The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at…

A: Our objective is to find the equation of tangent line to the curve at(2, 4) .

Q: Find the equation of the tangent line to the curve  at the given point . Sketch the curve and the…

A: The equation of the curve is y=-2x3. The point of contact is (-2, 16).

Q: Find the equations of the tangent line and normal line to the curve y = x3- 2x 1+ at the point (0,…

A:

Q: Find an equation for the tangent line to the curve at the given point. Then sketch the curve and the…

A: Given: y=8x, 16,32

Q: Find the equations of all lines through the origin that are tangent to the curve y = x³ – 6x2 – 2x.…

A:

Q: Find an equation of the tangent line to the curve at the given point. y = 7x2 - x3, (1, 6) y =…

A:

Q: Find the slope m of the tangent to the curve  y = 3/sqrtX  at the point where x = a > 0. m = ?

A:

Q: 2а3x at (a, a) ,2 x2+a²

A: Given curve is,

Q: Find equations for the tangent line and the normal line to the graph of the equation at the given…

A:

Q: Find an equation of the tangent line to the graph at the given point. (x + 2)? + (y – 3)² - 37, (-1,…

A: Differentiating with respect to x, we get Now slope of the tangent at (-1, 9) is

Q: Find the equation of the line tangent to the graph of x + y° = 2xy - 34 at (- 1, - 3). %3D The…

A: Equation of tangent line

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.