5. How many lines are tangent to both of the parabolas y = -1-x² and y = 1+ x?? Find the exact coordinates of the points at which these tangents touch the parabolas. Include an accurate sketch.

Q: Find equations of both lines through the point (2, –3) that are tangent to the parabola y = x2 + x.…

A: We have to find equations of both lines through the point (2 , -3) that are tangent to the parabola…

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

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Q: What is the equation of the tangent line to the circle x2 + y? = 34 at the point (5, 3)?

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

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

A: Given:

Q: Find the equation of the family of curves whose at any point (X, Y) is 1. 3x? + 4 2. * y X+1 3. y-1…

A: Here, there is a little word missing in sentence, 'Find the equation of family of curves whose slope…

Q: Draw a diagram to show that there are two tangent lines to the parabola y = x 2   that pass through…

A: Explanation: Given that,                     Assume that, point of tangency is (a, a2). Slope of…

Q: Determine the length of the tangent to the circle x2 + y2 − 4x − 5 = 0 from (8, −2)

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Q: Find the exact length of the curve. y = 7+ cosh (2x), 0 ≤ x ≤ 4 1 2

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Q: Find the point Q that is on the curve nearest %3D the point (4, 1)

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Q: Graph the parabola f(x) = x2 . Explain why the secant lines between the points (-a, f(-a)) and (a,…

A: We have the given equation of parabola as fx=x2 On considering the solution set, which satisfy the…

Q: (a) What is the equation of the line that is tangent to the circle of radius 9 at (0, – 9) and whose…

A: Given:  A circle x2 + y2 = 92.  ---------------------------------------------------------…

Q: Solve the center qnd radius of the circle passing through the points P(1,1) and is tangent to the…

A:

Q: Find the exact length of the curve.   36y2 = (x2 − 4)3,    5 ≤ x ≤ 6,    y ≥ 0

A: NOTE: Refresh your page if you can't see any equations. . but here

Q: Find the exact length of the curve. 36y2 = (x2 – 4)³, 4 < x < 9, y 2 0

A: Given:

Q: 1. Find the equation of tangents to the circle x² + y² = 9 with slope 1.

A:

Q: Let L be the tangent line to the parabola y=x2 +3 at the point (1, 4). The angle of inclination of L…

A: Given: Let L be the tangent line to the parabola y=x2+3 at 1,4. To Find: The angle of inclination of…

Q: Find an equation of the tangent line to the parabola y = x2at the point (2, 4).

A: To find the equation of the tangent line to the parabola y = x2at the point (2, 4). For the parabola…

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 5? a = b…

A: Given: The line 4x+y=b is tangent to the parabola y=ax2 when x=5. To Find: Value of a and b.…

Q: Find the length of the curve from the entire hypocycloid 2 2 x3 + Y³ = a³.

A: Explained below

Q: The slope of the tangent line to the parabola y 4x + 7x + 5 at the point (0, 5) is: The equation of…

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Q: The slope of the tangent line to the parabola y 3x? + 6x + 2 at the point (- 2, 2) is: The equation…

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Q: Find the exact length of the curve. 36y2 = (x² – 4)³, 4 < x < 9,

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Q: What equation is tangent to the circle (x-4)² + (y- 2)* = 25 at the point (8,5)?

A: concepts remember for this question are; 1. The general equation of a straight line is y = mx + c,…

Q: dy Use the method of isoclines to draw several solution curves for the equation dr

A: First integrate the function using variable separation method and find y as function of x  Then draw…

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: 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: A curve like Y = is called a serpentine. 1+2x2 3 n equation of the tangent line to this curve at the…

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Q: What equation is tangent to the circle (x-4)^2 + (y-2)^2=25 at the point (8,5)?

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Q: Q1/ Find the equation of the circle tangent at least to three lines (y = 1, y 5, x 2 and x = 7). %3D

A: We have considered the first 3 lines as the line of the tangents For more see below

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

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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: Identify the center and radius of the circle passing through the points P(1, 3) and is tangent to…

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Q: . Find the equations of both lines that pass through the point (2, –3) and are tangent to the…

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

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Q: What is the smallest possible area of the triangle that is cutoff by the first quadrant and whose…

A: Given that the triangle that is cut off by the first quadrant and whose hypotenuse is tangent tothe…

Q: What equation is tangent to the circle(x-4)^2 + (y-2)^2  at the point (8,5)?

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

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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: At what point of the parabola y=x -3x+5 is the tangent line parallel to the line 3x-y 2?

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Q: Find the equations of the tangents to the circle x² + y² = 9 with slope 1

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Q: 2. Circles with fixed radius r and tangent to the y-axis.

A: Solution is given below:

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: The figure shows a semicircle with radius 1, horizontal diameter PQ, and tangent lines at P and Q.…

A: As per the question we are given a circle of radius 1 and a horizontal line above the x-axis. Now we…