verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to the curve at the givenpoint. y2 - 2x - 4y - 1 = 0, (-2, 1)

Q: Determine the values of x where a curve y = x3 - 3x2 - 9x+ 12 has horizontal angent lines.

A: Given,         y=x3-3x2-9x+12

Q: Find the slope of the curve, equations of the tangent and normal lines to the given point. 8x y at…

A: Solution

Q: 5. Find the equation of the tangent and normal lines to the curve x = t2 – 2t, y= t3 - 3 when t =…

A: Firstly we find Slope of tangent and slope of normal to the given curves and then we will find…

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=1 and y=0 in the given equation So the point satisfies the equation

Q: Find the equation of the line normal to the tangent at the point (1,2) x’y+xy² = 6. on the curve

A:

Q: Find the slope of the tangent line to the curve (a lemniscate) 2 (z? + y?)° = 25(x² – y²) at the…

A:

Q: At what point on the Curve x = 3t2 + 4, y = t³ - 6 does the tangent line have slope (х, у) %3D

A:

Q: Verify that (2,3) is on the curve x²+xy-y²=1 and a. find the line that is tangent to the curve at…

A: Given curve, x^2+xy-y^2=1

Q: 1. Find the equation of the lines tangent and normal to the curve 3x?y2=4x2-4xy. at the point…

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

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: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: Given curve is The point (-1,3) lies on the curve if it satisfies the equation of curve Therefore,…

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A:

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

A: We have to find the point

Q: At what point on the curve x = 3t2 + 2, y = t3 – 2 does the tangent line have slope ? (х, у)

A: Slope of the line = dy/dx To get dy/dx, first get dx/dt then get dy/dt. Now divide dy/dt by dx/dt.5

Q: Find the equation of a line tangential to the curve y = 2x² + 7x + 9 at P(1,18).

A:

Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=1 and y=π/2 in the given function  Since both sides are equal so (1, π/2) is on the curve…

Q: Find the slope of the tangent line to the curve - 4x – 3ry + 4y° = = 14 at the point (- 3, 2).

A:

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

A:

Q: Determine the constant c such that the straight line joining the points (0,3) and (5.-2) is tangent…

A:

Q: find equation for the lines that are tangent andnormal to the curve at the given point.xy + 2x - 5y…

A: Given : The equation is x y + 2x - 5y = 2 and point (3, 2).

Q: verify that the given point is on the curve and find the lines that are (a) tangent and (b) normal…

A:

Q: Find the slope of the tangent line to the curve - 4a? – læy + 2y³ : - 4x² = - 4 at the point (2, 2).

A: to find the slope differentiate  the y with respect to x.

Q: The equation of the tangent line to the curve a? +y = 16, at (4,-13) is 4 13 13 (x – 4) + 13 4 4 y =…

A:

Q: Find the equation of the tangent line to the curve y=1-x² that is parallel to the line 2x-4y=8

A:

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: Determine the equation of the line tangent to the curve   at the point (-1,1) and reestablish a…

A:

Q: b) Find equation of line passing the point ( 4, -1) and normal to 3y+ x=1. ||

A:

Q: At what point on the curve x = 9t2 + 2, y = t3 - 6 does the tangent line have slope ? (x, y) = ])-

A: Consider the curve

Q: find equation for the lines that are tangent andnormal to the curve at the given point.x^3/2 +…

A: Given: x32+2y32=17    at the point (1,4)

Q: At what point on the curve x = 9t? + 9, y = 3 - 6 does the tangent line have slope

A: Given curves are And

Q: Find the equation for the line tangent to the curve 2exy = x + y

A:

Q: The equation of the tangent line to the curve +y =64, at (6,-12) is 12 y=D (-6)+12 6. 6. 12 -6) – 12…

A:

Q: Verify that the given point is on the curve and find the lines that are a. tangent and b. normal to…

A: Substitute the point (-3,-1) in the given equation.

Q: At what point on the curve x = 9t2 + 3, y = t3 – 2 does the tangent line have slope ? (x, y) =

A:

Q: At what point on the curve x = (x, y) 6t² + 5, y = t³ - 2 does the tangent line have slope 11/22

A: This question is based on finding slope of parametric curve.

Q: Find the slope of the tangent line to the curve - l2? – 2ay + 4y³ = - 249 at the point (1, – 4).

A:

Q: Find the slope of the tangent line to the curve - 6y3 – 42?y? = 2 at the point (1, – 1)

A: We have to find slope of the tangent line to the curve -6y3-4x2y2=2 at the point 1,-1

Q: Find the equations of the tangent and the normal at the point indicated. y = x2 - 2x at its…

A: Given that - y = x2 - 2x at its points of intersections with the line y = 3

Q: Find the equation of the tangent and normal lines to the curve y=sqrt(x) at the point (1,1).

A:

Q: Verify that the given point is on the curve and find the lines that are (a) tangent and (b) normal…

A:

Q: At what point on the curve x = 9t2 + 6, y = t3 − 9 does the tangent line have slope 1/2?

A: Given parameteric equations of curve,   .x = 9t2 + 6 , y = t3 – 9   To find the point on curve…

Q: . Determine the points where the curve 6x+ 4y-y=6 has a vertical tangent line. p. Does the curve…

A:

Q: Find the equation of the tangent and normal line using the stipulated conditions   2.) x2 + 2y2 =…

A: The equation of tangent line is x2+2y2=9⇒x29+y292=1we have a=3 and b=92Since, we know that the…

Q: Find the equation of the line that is normal to the curve (y-x)2 = 2x + 4 at (6,2). %3D

A: Use equation of normal line

Q: or the curve x²y²=9 at (1,3) find the equation of normal line

A: Given: x²y²=9

Q: The equation of the tangent line to the curve a? +y = 25, at (8,-12) is. 12 (x+8) – 12 8 y = 8. y =…

A:

Q: Find the slope of the tangent line to the curve 2x + lay 4y 20 at the point (2,- 2).

A:

Q: Find the slope of the curve, equations of the tangent and normal lines to the given point. y = x3 –…

A: We have to solve the problem

Q: At what point on the curve x = 3t2 + 1, y = t3 – 5 does the tangent line have slope ? 2

A: