For what values of c is there a straight line that intersects the curve y = x' + cx' + 12x² – 5x + 2 in four distinct points?

Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

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Q: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: 2 Find the line tangent to the curve r3 +y3 at the point 4 (-3/3, –1).

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Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y=xn

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Q: 4. At what point on the graph of y =x2 is the tangent line parallel to the line 2x – 4y = 3?

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Q: Find the length of the curve defined by 2? = 2y3 from x = 0 to x = 4:|| %3|

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Q: The slope of the line tangent to the graph of y = In(x²) at x = e² is %3D

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Q: The equation of tangent line to the graph of 8x²+16y²=48 at (2,1) is A x- y - 3=0 x- y+3=0 c none of…

A: Slope of tangent line is y'

Q: Find the equation of a tangent line to the curve y= 2x3 - 3x2 - 10x +1 which is perpendicular to the…

A: The equation of the line is      x+2y-6=0⇒y=-12x+3       in the form of line equation y=mx+c  So,…

Q: 18- What is equation of the tangent line of ƒ(x)=x³- 2x² - 1 at the point x = 2 ? y=-2x+9 1903…

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Q: What is the equation of the line normal to f(x) = 5x5 – 2x at x = -1 %3D

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Q: 2. Find the equation of the tangent line to the curve y = x2 - 2x -3 that is parallel to the line x…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: The curve y = a x 2 + b x + c passes through the point ( 1 , 2 ) . The line y = 2 x + 1 is tangent…

A: Given that the curve passes through a point.

Q: The tangent of the curve x^2+y^2--7 * 2xy3DO at the point (1,1), is a. y-2-х. О b. y=x-2. O С.…

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Q: Find the line tangent to the curve x + yi = 4 at the point (3V3, –1). y = x- 4 Oy = x+4 y = O y= s…

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Q: Find the condition that the line ax+by =1 may be normal to the curve an-1y =xn

A: Given thatan-1y =xn Solution is as follows

Q: Find all points on the graph of 3x 2 + 4 y 2 + 3xy = 24 where the tangent line is horizontal

A: Given:              3x2+4y2+3xy=24 We know the tangent line is horizontal when y'=0 So we want to…

Q: A line is tangent to y = x - 2 at (2,6). What is the coefficient of x when the line is in the form…

A: Given curve y=x3-2    ;   (2,6)

Q: Find the tangent and normal line to the curve at the specified condition. 12x2 - 20y2 = 55 parallel…

A: Given that the curve is 12x2-20y2=55 and the required tangent and normal line is parallel to the…

Q: Determine the slope of the tangent line to the graph of x2 + 4y2 = 4 at the point (√2, −1/√2).

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Q: Find an equation for the tangent line to the curve y = xV 2x² - 14 at the point (3,6). O y- 6 = 14(x…

A: The equation of the tangent line to the curve is, y - 6 = 11(x - 3)  The detailed solution is as…

Q: 20. Does the line that is normal to the curve y = x² + 2x - 3 at the point (1, 0) intersect the…

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Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: 3) Calculate the length of the curve interval [-2₁2]. y = x²/2 on the

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Q: Find all points (x, y) on the graph of y = x/(x - 2) with tangent lines perpendicular to the line y…

A: Given:

Q: Show that the solution of the equation YUx – xUy = 0 containing the curve x² + y² = a², u= y, does…

A: Given that y ux – x uy = 0, The Lagrange’s auxiliary equation for the given equation is given as:…

Q: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: The tangent line to the curve y = 1/3x^3−3x^2+9x+12 is parallel to the line 8x−2y=3 at two…

A: given: the tangent line to the curve y=13x3-3x2+9x+12 is parallel to the line 8x-2y=3 at two points…

Q: Calculate the length of the curve defined by x =- Vy(y-3)on the interval 1 < y < 9.

A: x=13yy-3,   1≤y≤9 Differentiating with respect to y, we get…

Q: B. Find the length of the curve y = x² from x 0 tox = 4.

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Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

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Q: Find the length of the curve 9y2=8x3 from x=o to x=12 when y>0

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Q: Make the curve y=ax²+bx+ c pass through (2,1) and be tangent to the line y=2x+4 at (1,6)

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Q: (3) Find an equation of the tangent line to the curve y = 2x² + 3 that is parallel to the line %3D…

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Q: At what values of x on the curve y= 2x³+13x²+5x+9 does its tangent lines pass through the origin? In…

A: Given equation of curve: y=2x3+13x2+5x+9……1

Q: The line that is normal to the curve x + 3xy - 4y² = 0 at (3,3) intersects the curve at what other…

A: Given: x2+3xy-4y2=0 at (3,3)

Q: 2) Find the tangent line to y2 = x at the point (4, –2).

A: Given: y2=x…

Q: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

Q: 2. Find the equation of the tangent lines and the normal lines to the curve y = 2x² +3 at the point…

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Q: Find the length of the curve for 12x = 4y³ + 3y-¹ where 1 ≤ y ≤ 3 Enter your answer in exact form.…

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Q: Find the length of the curve between the specified interval: 3/2 a. y = x7² from x = 1 to x = 4 b. y…

A: (a) Given curve: y=x32 Interval x=1 to x=4 The length of the curve is given by the formula:…

Q: A tangent line to the curve c(t) - (- 4t - 5t + 2, t - 15t - 1) has slope 3 at the pointias) 2-1…

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Q: Find all points ( x,y) on the graph of f(x) = 3 x² – 4x with tangent lines parallel to the line y=…

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Q: What is the equation of the curve that passes through the point (0, 3) and has a slope at any point…

A: We have to find

Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

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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: Show that the line y = -10x + 20 is tangent to the curve y = x4 – 4x^3 – 5x^2 + 26x – 16.

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Q: 12)What is the slope at (1,2) for curve define by xy^2=4?

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Q: 5. Find the point on the parabola y=2x-3x+6 where the tangent line is parallel to the line 7x+y=1.

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Q: What is equation of the line normal to graph of y = x^3 + 3x^2 + 7x - 1 at the point where x = -1? O…

A: Solving the problem by finding the normal of the given equation.

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.