Let the line y = mx + 2 be a tangent to the curve y = In-, at the point P. i) Find the coordinates of P. ii) Find the value of m.

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: 2. Assume the lines that appear to be tangent are tangent. Find ZW. Y 12 X 20 ZW =

A: Theorem  The tangent at any point of a circle is perpendicular to the radius through the point of…

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: A stream line is a line that is everywhere tangent to the velocity filed ylgn O ihi 0

A: A stream line is a line that is everywhere tangent to the velocity filed

Q: (b) Find a , b and c if the curvey = x + a x + b and y =c x + x have tangent lines paralle to each…

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Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: A stream line is a line that is everywhere tangent to the velocity filed ylgn O İhi O

A: Given that A stream line is a line that is everywhere tangent to the velocity field

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

A: Given

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

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Q: What is the angle between the curves y = x2 and y = x4 at their point of intersection?

A: We have find the angle between the curves y = x2 and y = x4 at their point of intersection we have,…

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

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Q: There are exactly two tangent lines from an exterior point to a circle. True or False? O True O…

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Q: :If the tangent at (a, b) to the curve x³ + y° = c° meet the curve again in (a,,b,). b, Prove that…

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Q: 4. y = x2--Inx x = 1 ve x = e

A: Topic- application of derivatives to find angle between curves

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: Show that if P lies on the intersection of the two curves x2 − y2 = c and xy = d (c, d constants),…

A: Solution:Givenx2-y2=c     and   xy=dTo prove tangent curve at P are…

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: Find the points on the lemniscate where the tangent is horizontal. 8(x2 + y2)2 = 81(x2 − y2)

A: The equation for the lemniscate

Q: Find the slope of the tangent line to the "tilted" ellipse at the point (-1, 1). x²+ y² = xy+3 3 3…

A: To find the slope of the tangent line to the ellipse x2+y2=xy+3 at the point -1,1

Q: Assume the lines that appear to be tangent are tangent. Find ZW. Y 12 X 20

A: ZW is the radius of the circle. According to tangent, the tangent theorem states that a line is a…

Q: The projectile is thrown at the angle of 45 degrees with the initial velocity of 1 meter per second.…

A:

Q: Find the length of the curve. 2,3/2,0 st s9 x= 4t, y 3 61 242 2 3 O 2. seçenek 4. seçenek 122 61 3 3…

A: We can find the arc length as below

Q: Find the path of the sloping path y = x² + c such that θ = π / 4 is the angle between the tangents…

A: Slope = 1  Point are (a,b) So equation of tangent      Y-b = 1.(x-a)

Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

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Q: Show that the tangents to the curve y2 = 4px from any point on the line x = -p are perpendicular.

A: The given curve is,

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

Q: 9. 15 16

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Q: Find the exact length of the curve. x = et − t,    y = 4et/2,    0 ≤ t ≤ 2

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Q: on of the tangent to y = 3e" + 3ex that is parallel to

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Q: A coast artillery gun can fire at any angle of elevation between 0° and 90° in a fixed vertical…

A: A coast artillery gun can fire at any angle of elevation between 0° and 90.

Q: Find the acute angle 0 between the curves C1 and C2 given by C1 : y = x2 , C2 : y = x³ (1) at their…

A: Please refer the attached image for complete solution.

Q: An airplane is traveling at a speed of 130 km/hr with a bearing of 10° at a fixed altitude with…

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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 equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: At what point is the tangent line to the curve y³ : = 6x² perpendicular to the line 2x + y = 2 = 0?…

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

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Q: Give the equation of the tangent plane to each of these surfaces at the point indicated.

A:

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: (is)Find the eguakion af the line tangent to y=ro* át (!,10')

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

A: Now when x = 3, we get Therefore the point (3, -4) is on the given curve. a). Slope of the tangent…

Q: At what points do the curves y=x2 and y=√x intersect? Find the angles of intersection between the…

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Q: The curve y = ax? + bx +c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: Explanation of the answer is as follows

Q: Find the angle of intersection between the curves y = x- +1 and y = x+x-

A: y = x2 + 1,y = x+ x-1Points of Intersection;x2 + 1 = x+1xx(x2+1) =(x2+1)x = 1y = 2point of…

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

A:

Q: What is the slope of AC in right triangle ABC shown in the standard (x, y) coordinate plane above?

A: Given,         A right triangle ABC is shown below :

Q: where c is a constant, then prove that the foot of perpendicular from the origin upon the straight…

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