27. The equation of the common tangent to the circles x+ y - 12x- 2y-123D0 and x*+y - 4x + 4y + 4 0 at the point of contact is A. 4x + 3y + 8 =0 B. x+3y +1=0 C. 4x+ y+8 +0 D. 4x-3y +8=0

Q: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and

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Q: 2. Find the equations of tangents that can be drawn from the origin to the circle x² +y-2x+8y+2=0.

A: Given below the detailed solution

Q: Find the length of the curve on y=2x^(3/2) from x=0 to x=1

A: Explanation of the solution is given below...

Q: Find the exact length of the curve. y = 3 + 2x^(3/2), 0 less than x less than 1

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Q: Find an equation of the tangent line to the graph 16x4 + y4 = 32 at the point (1,2). %3D 1) 5 1 -+x-…

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Q: How do I do this?

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Q: Find the slope of the tangent line to the circle 4x² + 9y² = 36 at the point (0,2).

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Q: How do you find the equation of the tangent line to the parabola for y = x2 − 3x − 1 at x = 4.

A: The equation of the given parabola is y=x2-3x-1. We have to find the equation of the tangent line to…

Q: Find the points on the graph of y = 1– 5x + 3x² where that tangent line is parallel to the line y –…

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Q: The slope of the tangent line to the parabola y = 2x + 2x + 6 at the point (- 1, 6) is: The equation…

A: The slope of the tangent line to the parabola                      y = 2x2 + 2x + 6 at the point…

Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4)

A: Equation of the tangent line

Q: 13. Show that the length of the portion of any tangent line to the ball x2/3 + y2/3 cut off by the…

A: Given: The equation of the ball is: x23+y23=a23...........(1) We have to show that the length of the…

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: Find the length of the curve defined by y = 3z3/2 - 3 from x = 3 to a = 9. The length is

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Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

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Q: Find equations for the lines tangent and normal to the cissoid of Diocles y (4 – x) = 9x° at (2,6).

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Q: The slope of the tangent line to the parabola y = 2x“ + 2x + 6 at the point (1, 10) is: The equation…

A: Given,            The parabola is y=2x2+2x+6 and the point is 1,10.

Q: At what point of the parabola y = x² – 3x – 5 is the tangent line parallel to 3x - y = 3? O (-3,-5)…

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Q: 15. When a line L is tangent to the circle 2 + v = 100 at the point (a, 6), find the equation of…

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Q: 4. Find the exact length of the curve. 36y2=(x²-4)3,2≤x≤3.y≥1

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Q: Show that no point on the graph of x 2 - 3xy + y 2 = 1 has a horizontal tangent line.

A: Given  x 2 - 3xy + y 2 = 1

Q: 4. The tangent of the acute angle between the linesy = 4x – 3 and y = x - 5 is Tano 144() 13 3

A: Please rate

Q: 6. Show that the line with equation y = 3x – 5 is a tangent to the circle with equation x² +y? + 2x…

A: Equation of line : y=3x-5 Equation of circle : x2 + y2 +2x -4y -5=0 We have to prove that the line…

Q: find the length of the curve 3y2=4x3 from x=0 to x=8 when y greater than or equal to 0.

A: The formula for length of a curve f(x) extending from point a to point b is given as,

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: The line that is normal to the curve x + 2xy - 3y = 0 at (4,4) intersects the curve at what other…

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Q: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

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Q: The tangent to the circle x2 +y2 +10 x+5 y= 60 at the point (2 ,4) is Select one: O None O 13 y +…

A: Given that:x2+y2+10x+5y=60

Q: Find the equations of the tangent lines to the circle (x + 2)² + (y + 2)² = 25 at the two points…

A: At x=2; (2+2)2+(y+2)2=25 16+(y+2)2=25 (y+2)2=9 y+2=±3y = 1 or -5Therefore two points at which…

Q: What is the equation of the line tangent to the graph of y = (2x+3)/(3x-2) at the point (1,5)? 13x -…

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Q: Make the cubic y = ax3+bx2+cx+d pass through the points (0,-6), (1,-2) and be tangent to the line…

A: This is the simple question based on algebra and derivative which could be solved using the basic…

Q: 2 Show that the line y = x +3x+m for all values of m. y= mx+4 will touch or intersect the curve

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Q: Find the length of the tangent to the circle x² + y² − 2x − 3y − 1 = 0 from the point (2, 5)

A: Solution- The equation of the circle x2+y2-2x-3y-1=0 The point =2,5 length of the tangent

Q: 2 Consider the two graphs y = 2x and x - xy + 2y = 28. The absolute value of the tangent of the…

A: Introduction :

Q: For what values of a and b is the line 2x + y = b tangent to the curve y = ax² when x = 4?

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Q: please show in your solution how to get the pt of intersection between curves  y=(x)^1/3 and…

A: Point of intersection of the curves is the point where two curve intersect .

Q: What is the sum of the abscissas of the points where the tangents of the y=(1/3) x^3-(3/2) x^2 – 2x…

A:

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 4?

A: Consider the equation of the parabola, y=ax2 differentiate the equation with respect to x to find…

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: Find the exact length of the curve. 36y² = (x²-4)³, 4≤x≤6, y 20

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Q: IFind the exact length of the curve x= 3t -t, y=3t² ,0<t<2 ||

A: We have to find the exact length of the curve. The length of the curve is given by

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: 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.

Q: 10. At what point on the parabola y = 3x² + 2x is the tangent line parallel to the line 10x – 2? y

A: Given,          The parabola y=3x2+2x is the tangent line parallel to the line y=10x-2.

Q: Situation 8. Find the tangent to the cubic y = x³ – 2x + 3 parallel to the line 10x – y = 3. 28. m =…

A: Tangent to the cubic and slope

Q: Find the exact length of the curve. 36y² = (x²-4)³, 5≤x≤9, y 20

A:

Q: 4. Find the equation of the circle that is tangent to the line x = 8 that has a center at (-5, 10).

A: The general equation of circle having the center at h,k and radius r is given as, x-h2+y-k2=r2 it is…

Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.