) Find equations of the tangent line and normal line to the given curve at the specified point.  y = 6xex,  (0, 0) 2) Find the points on the curve where the tangent line is horizontal. y = 2x3 + 3x2 − 12x + 9 3) Draw a diagram to show that there are two tangent lines to the parabola y = x2 that pass through the point (0, −4). Find the coordinates of the points where these tangent lines intersect the parabola.

Q: Determine the latera recta length of the curve 9x² + 25y² - 225 = 0

A: Solved below

Q: Find the exact length of the curve. x- 2, y=? - 2, Osts 6

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

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: 3) Let M be the midpoint of a line segment joining two points A(20, -1) and B (4, –9). Calculate the…

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Q: 4. Find the equation of the locus of the points P(x, y) whose distances from the point (3,2) are…

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Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: Find the exact length of the curve. x- 2, y =? - 2, Osts9

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Q: Find all points with coordinates of the form (a, a) that are a distance 3 from P(-2, 1).

A: Given: P(-2,1) and distance is 3. To find the other coordinate point.

Q: 1. Find the distance between the points P = (-1,3) and Q = (4, -2). Find the midpoint of the line…

A: Consider two points Px1, y1 & Qx2, y2 Then, the distance between the points PQ is given by:…

Q: The end points of line segment 4, which lies in the xy-plane, are (-2, 5) and (6,-3). Which of the…

A: i have used the formula of midpoint of the two points and the slope point form of the straight line…

Q: x = e2t – 1, y = et

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Q: 4 Find a. the equations of the tangents to the circle x'+y +4x-2y-24 0 at the points where the…

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Q: The curve y et and the lines y = 0, x = 0, and x = In 2 %3D

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Q: 1. Find the point on the line 1 - a that is closest to the origin.

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

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

Q: Suppose the midpoint of RT is M = (3,0). If point R has the coordinates of (-1, 4), what are the…

A: Given midpoint RT is M =(3,0)

Q: Q.5 Find the length of the line segment connecting points A and B located at (-2,5)(1,1)…

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Q: (b) Eliminate the parameter to find a Cartesian equation of the curve.   for  −5 ≤ y ≤ −1

A: The parametric equation of curve are x=1-t2 y=t-3

Q: Suppose that receiving stations X, Y. and Z are located on a coordinate plane at the points (5,10).…

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Q: Consider the two points (4, –3) and (5, 7). The distance between them is: The x co-ordinate of the…

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Q: 4. Suppose you are given equations of two overlapping circles as a. Determine how to find the points…

A: If two circles are  overlapping then we find  two points of intersection.

Q: Sketch parallelogram-INDY with diagonals intersecting at point P in the box below on the left. If IP…

A: Given,           A parallelogram INDY with diagonals intersevting at point P.           IP=3x,…

Q: 7. Eliminate the parameter to find a Cartesian equation of the curve: x = Vt, y = 5 – 3t

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Q: In Problem,find the distance from P1 to P2.

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Q: 34. Find the points where the line y = 2x intersect a circle of radius 6 centered at the origin.…

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

Q: Assume that lines which appear to be tangent are tangent. Solve for the unknown side. 10. 11. 12 16…

A: We have to find the missing length of triangle.

Q: 253. Find the distance between point A(-3, 1, 1) and the line of symmetric equations x=-y=-z.

A: Let B(a,b,c) be a point on a given line with direction vector v⇀=(x,y,z). Then distance of  a point…

Q: The points P, Q and R have coordinates (8, 7), (−2,−1) and (−6, 5) respectively. Show that the…

A: The point P is (8,7) and find the equation of the line passing through the point (8,7).The line…

Q: 1. Find the distance between the points P = ( - 1, 3) andQ = (4, - 2). Find the midpoint of the line…

A: Given :  P = ( - 1, 3) and Q = (4, - 2) we have to find the distance between the points also find…

Q: Eliminate the parameter to obtain an equation in x and y: x=-2cos2t, y=-2sin2t

A: x=-2cos2t y=-2sin2t using trigonometric property,               sin2t+cos2t=1

Q: Demonstrate that the circles (x – 2)? + y² = 2 and x? + (y – 2)2 = 2 share tangent at point (1, 1),…

A: Here we will apply the concept of finding the equation of tangent to the two circles at point (1,1).

Q: 4 Find a. the equations of the tangents to the circle x +y + 4x – 2y – 24 = 0 at the points where…

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Q: Draw a diagram showing two perpendicular lines that intersecton the -axis and are both tangent to…

A: The given parabola equation , y=x2. To draw two perpendicular lines that intersect on the axis and…

Q: Find the points on z the point (1, 2, 3) axis which are at a distance /21 from

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Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

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Q: ind an equation of the line that passes

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

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Q: Show that the point is on the unit circle. (2-) We need to show that the point satisfies the…

A: Equation of unit circle is x²+y² = 1

Q: Exer. 35-36: Find equations of the tangent line and normal line to the hyperbola at the point P. 35…

A: As per guideline we have to solve one question

Q: Consider the two points (4,2) and (10,4). The distance between them is:   The x co-ordinate of the…

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Q: Consider point P (4, 2) and line /with equaiton -3x + 4y = 6. The equation of the line that passes…

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Q: (A) Find the unique point P on the y-axis which is on both planes. (–, ,

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

Q: If point P(2,3, a) is on this tangent plane, find a.

A: The equation of the tangent plane to the surface z=f(x,y) at the point (a,b,f(a,b)) is

Q: A curve on the ry-plane passes through the point (0, a) for some number a, and has the property that…

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Q: A curve C has equation y =x2lnx- 2x +5, x > 0. %3D For which values of x, the curve C is convex?

A: The equation of the given curve is  y=13x2 ln x-2x+5 , x>0 For the curve to be convex its second…

Q: 4 Find a. the equations of the tangents to the circle x +y +4x-2y – 24 = 0 at the points where the…

A: Given,  (a) Equation of the circle   x2+y2+4x-2y-24 = 0  We have to find the equations of tangents…

Q: Consider the two points (1, –4) and (-6, –2). The distance between them is: The x co-ordinate of the…

A: By using distance formula and mid point formula, we calculate the required distance and midpoint.

Q: Find the length of the tangent to a circle from point of tangency to point (8,2) . The circle is…

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