If c > 5, how many lines through the point (0, c) are normal 29 lines to the parabola y = x²? What if c <

Q: What is the families of the curve of all straight lines through the fixed point (h,k).

A: The differential equation representing the families of curve of all straight lines through the fixed…

Q: Find the points where the tangent is parallel to OX. y = x4 - 8x3 + 22x2 - 24x + 9

A: Given: y=x4-8x3+22x2-24x+9.

Q: Find the shortest distance from the point x = (-3, 0, -12)  to the line r = t(0, -2, -2).

A:

Q: Find the exact length of the curve. 글 cosh(2x), sxs8 y = 4 +

A: Given:

Q: What is the length of the curve y= x3/2+4 from the point (1,5) to (4,12)?

A: Arc length is defined as the distance between two points on the curve. It is done in such as way…

Q: When is the line ax+ by = c parallel to the y-axis? To the x-axis?

A: ax+by+c=0        When a=0, then the line equation becomes               bx+c=0…

Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13=0 in which the tangent line…

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Q: Find the envelope of the family of straight lines, which together with the line segments intercepted…

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Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x, y) = |

A: To find - Point on the given line closest to the origin.

Q: 4:x=1+21, y =-2+t, z=4-t 1, :x = 5–3s, y= 4- z = 2+

A:

Q: Find the distance from the point (0, 0, 0) to the line x = 5 + 3t, y = 5 + 4t, z = -3 – 5t.

A: Find the distance.

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

A:

Q: For what values of a and b is the line-3x + y-b tangent to the curve y = az3 when x-5? a=

A: The value of slope of tangent to the curve at the point is the value of its derivative at that…

Q: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

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Q: Find the distance from point P to line L.  P(3,-1,4), L: (x-4)/-1 = (y-3)/2 = (x+5)/3

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Q: I need a paragraph proof for proving that a circle and a line cannot intersect in three or more…

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Q: Find the point on the line y=5x+3 that is closest to the origin (x,y)=(______)

A: Let (m,n) be the point on the line which is closest to the origin.Put n = m, y = n, in y = 5x + 3…

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: an equation for line L in point-s erpendicular to y 5x. 6Ty=5x (1,5) 2- -4 -2 4 6 2.

A: We will solve the problem

Q: The distance between the points (3, 6) and (x, 5) is 7. What is/are the coordinate(s) ofx?

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: Find the points on the graph of circle defined as (x – 1)2 + (y + 3)2 = 16 where the normal line is…

A:

Q: What is the length of the curve y3/2+4 from the point (1,5) to (4,12)?

A: To find: The length of the curve y3/2+4 from the point (1,5) to (4,12).

Q: What are the coordinates of the points in the graph of y2-x²+6x – 13=0 in which the tangent line is…

A: To find the points at which tangent line is horizontal , y' =0.

Q: A line with slope m passes through points (p, q) and (r, ?_).

A: The complete statement: A line with slope m passes through points p,q &amp; r, ?

Q: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

A: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

Q: Find the distance from the point (1, 5, 5) to the line x = 0, y = 5 + t, z = 5 + 5t.

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Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

A: The functionals with in the calculus of variations are of the form V[f(x)]=∫abF(x,y(x),y'(x))dx The…

Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13= 0 in which the tangent…

A:

Q: Find the shortest distance from the point (- 1, – 2, 5) to the cone z = x² + y². Please | round to…

A: Distance of a point from cone is                                      d=(x-x1)2+(y-y1)2+(z-z1)2 from…

Q: Find the point on the line y = 4x + 3 that is closest to the origin. (x, y) =

A:

Q: Determine the equation of the line passing through the point (3,22) which minimizes the area of the…

A: This question is based on application of Derivative. The two-point form of a line passing through…

Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x,y)=

A:

Q: Find the shortest distance between the point Q (2, 0, 0) and the line determined by the points P1(0,…

A: Find the shortest distance between the point Q (2, 0, 0) and the line determined by the points P1(0,…

Q: 4. Find the equation for the line tangent to (persamaan garis şinggung) a. y= x2- 3 x + 5 at the…

A: The objective of the question is determine the equation of the tangent line.

Q: Find the point P on the line y=3x that is closest to the point (40,0). What is the least distance…

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

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Q: Find the point on the line y = 4x + 3 that is closest to the origin. (х, у) %3D

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Q: Find the equations of the tangent lines to the circle x2 + y2 = 9 which pass through the point (-7,…

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Q: The students in Ms. Logan’s class were asked to construct a line perpendicular to line through point…

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Q: What is the approximate distance between point L (6, 10) and point M (18, -14)?

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Q: For what values of a and b is the line 4x+y=b4x+y=b tangent to the curve y=ax3y=ax3 when x=5x=5? a=…

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Q: Find the distance between the line x + y + 2 = 0 and the point (1, 1).

A: The distance between the line ax+by+c=0 and the point x1,y1 is given as below. d=ax1+by1+ca2+b2

Q: How many lines are tangent to both of the circles  x2 + y2 = 4  and  x2 + (y − 3)2 = 1?   At what…

A: Given: The equations of circle are given as, Consider the parametric co-ordinates for the Eq. (A)…

Q: What are the coordinates of the points in the graph of y-x²+6x – 13=0 in which the tangent line is…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 19. Find the point on the line y= 2x + 3 that is closest to the origin.

A:

Q: Suppose that L is a line through the points (a, 2, c) and (3, –4, 2) that is parallel to one of the…

A: Given that: L is a line passing through (a,2,c) and (3, -4, 2) and parallel to one of the axes.

Q: A line that is normal to the curve x^2+3xy-4y^2=0 at (6,6) intersects the curve at what other point?

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Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

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Q: What is the midpoint between points (4, 7) and (1, 1)? Enter your answer in the boxes.

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.