4. Let C be a circle centered at (1,3) and is tangent to line at point P(2,3 - V3). (a) Find an equation of the circle C. (b) Find the slope-intercept form of the equation of line .

Q: Find an equation of the tangent to the circle x2+y2=36 at the point (5,3)

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Q: Determine the angle between the curves 2x=y2 and x2+y2-5x=0

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Q: what is an equation of a circle whose center is at (2 -4) and is tangent to the line x=-2

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Q: How do you find a tangent line of a circle Equation: (x - 3)2 + (y - 5)2 = 5 Point: (4,7)

A: solution:- Given                x-32+y-52=5                 point  4,7The above lies on the…

Q: a curve like y=x/1+1x^2 is called a serpentine. Find an equation of the tangent line to the curve…

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Q: Find the equation of the locus of the center of the circle which moves so that it is tangent to the…

A: Find equation of locus :

Q: Find the point in the first quadrant where the line y=4x intersects a circle of radius 5 centered at…

A: Equation of circle : x-h2 + y-k2 = r2 ; where (h,k) is center and 'r' is the radius .

Q: Find the exact length of the curve = √(y - 3), 1 ≤ y ≤

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Q: Describe the curve generated by x = 3 + 2t, y = -12 - 6t, for - ∞ < t < ∞.

A: Given: x=3+2t y=-12-6t            - ∞ < t < ∞ To find: curve generated by given functions.

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

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

A: Equation of the tangent line

Q: Sketch the graphs of y = x2 and y = −x2 + 6x − 5, and sketch the two lines that are tangent to both…

A: Given y=x2........... (1) and  y=-x2+6x-5 ..... (2) Sketch the graph using equation 1 and 2  Here…

Q: How to find an equation of the line tangent to the circle x^2+y^2-6x-2y-15=0 at the point (6,5) ?

A: Note:- The standard form of equation of tangent line at point c, d is y-d = m x-c Here, m is the…

Q: A circle is tangent to the line 2x-y+1=0 at the point (3,5) and the center is on the x+y=9. Find the…

A: Given that equation of tangent to the circle is  2x-y+1=0 at point (3,5)

Q: Find thepoints on the curve y = 2x3 - 3x2 - 12x + 20 where thetangent line is parallel to the line y…

A: Given curve is y=2x3-3x2-12x+20 Given line is y=2-12x=-12x+2  Slope of the given line is -12.…

Q: At which points on the curve y = 1 + 40 x3  - 3 x 5  does thetangent line have the largest slope?

A: The given equation of the curve is y=1+40x3-3x5. The slope of this given curve is given by its…

Q: find the equation of line tangent to the circle (x-1)2+(y-1)2=25 at the point (4,-3)

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Q: Find an equation for a line that is tangent to the graph of y = ex andgoes through the origin.

A: To find the equation of a line that is tangent to the graph of y=ex and passing through origin.…

Q: Find an equation of the line which is tangent to the circle r +y - dr + by – 12 = 0 at the point (5,…

A:

Q: Find thepoints on the curve y = 2x3 - 3x2 - 12x + 20 where thetangent line is perpendicular to the…

A: Given: The curve is y = 2x3 - 3x2 - 12x + 20 and the tangent line is perpendicular to the line y =…

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

A: We have to find the equation of the tangent to the circle x-42+y-22=25 at the point 8,5.

Q: Find the equation of the tangent line to the circle at the point (-3, -4). Equation of the circle *…

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Q: Find the equation of the tangent line to the circle x^2 +y^2 =1 13 at the point ( 1/2 , (√3)/2 )…

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Q: The family of curves orthogonal to ye2x = c is the family of curves whose general equation is?

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Q: The slope of the line tangent to the circle x' + y = 100 at the point (- 6,8)is

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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 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: Determine the equations of the tangent and normal line to the circle at each given point. 2 + y = 36…

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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 equation of line tangent the circle x ^ 2 + y ^ 2 = 25 at point at (3, - 4)

A: Differentiate the equation and get slope of tangent at (3,-4) ddxx2+y2=ddx252×3+2×-4×dydx=0dydx=34

Q: determine the general form of equation of the line that is tangent to a unit circle at a point 30…

A: Given: An unit circle with center at origin and a point P on the circle at angle of 30° in the…

Q: 5 Find the equation of line tangent the circle x+y = 25 at point (3, -4). .2 %3D

A:

Q: Verify that the two families of curves are orthogonal, where C and K are real numbers. Use a…

A: xy=C,  x2-y2=K Consider, xy=C Differentiating with respect to x, we get…

Q: Find the equation of a line tangent to a circle whose equation is x2 + y2 – 4x - 21 = 0 at point…

A: Let's.

Q: Find the standard form of the equation of the circle tangent to both axes at (-3,0) and (0,3).

A: Given that: The circle is tangent to both axes at (-3, 0) and (0, 3)

Q: ind an equation of the circle with centre C(3,-2) and tangent line y=5 .

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Q: Find the distance between the point (1,1) and (3,9) along the curve y=x2

A: Given:The points (1,1) and (3,9) along the curve y=x2To find the distance we need use calculus as…

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

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Q: Find the equation of one of the tangent lines to the circle x2 + y2 = 52 that pass through the point…

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Q: . Determine the points where the curve 6x+ 4y-y=6 has a vertical tangent line. p. Does the curve…

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Q: Find an equation of the tangent to the circle x 2 + y 2= 25 at the point  (3,4)

A: x2+y2=25 Differentiating with respect to x, we get 2x+2y·dydx=0⇒2y·dydx=-2x⇒dydx=-xy Now slope of…

Q: Find the equation of tangent to the circle 2x2+2y2+3x-4y+1=0 at (-1,2)

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Q: Find the equations of the tangent lines to the circle x2 + y2 = 1 which pass through the point (-4,…

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

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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: 2. Find the equation of the tangent to the circle x2 + y2 +4x +16y - 32 = 0 through (4, 0).

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