Use the Distance Formula to show that the circle with center (0, 0) and radius length r has the equation x + y = r.

Q: Find the equation of a circle centered at (1, −1) and tangent to the line 2x + 3y = 12

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Q: Form the diffrential equation of the family of circle having a centre on y-axis and radius 3 units.

A: the objective is to find the differential equation of the family of circles having centre on y axis…

Q: Evaluate the line itegral where C is the upper half of the circle z +y = 3.

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Q: Calculate (2 + x²y) ds where C is the upper half of the circle x² + y? = 1 (y>0) -1

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Q: Find the distance from the point (5,8) to the circle x2 + Y2 + 2x + 6y + 3 = 0

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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: Use the arc length formula to find the length of the curve y = 3x – 5, -2sxs 3. Check your answer by…

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Q: Use the arc length formula to find the length of the curve y = 3x – 4, -3 < x < 2. Check your answer…

A: This question is based on application of coordinate geometry.

Q: Use the arc length formula to find the length of the curve y = 7- 4x, -1sxs 3. Check your answer by…

A: It is known that arc length of any curve is given by the integral, We have,

Q: Find a formula for the distance from the point P(x, y, z) to the a. x-axis.    b. y-axis    c.…

A: The formula for distance between two points (x, y, z) and (a, b, c) is

Q: Evaluate xy ds where C is the right half of the circle given by x² + y² = 16 (i.e., the portion of…

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Q: Use Green'sTheorem to evaluate O ydx – xdy where C is the circle with center at the origin and…

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Q: Use the arc length formula to find the length of the curve y = 5x - 4, -1 <x< 3. Check your answer…

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Q: Set up and simplify (but do not evaluate) : 3x ds, where C is the arc of the circle r2 + y² = 4 from…

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Q: Use the arc length formula to find the length of the curve y = 5 - 4x, -15 xs 3. Check your answer…

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Q: Demonstrate that the circles (x- 2)² + y² = 2 and x? + (y – 2)? = 2 share tangent at point (1,1),…

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Q: In the diagram, SR is tangent to the circle at Q. If mPMQ = 212, what is mLPQR? м R 2.

A: 2. The figure of the circle is given by To evaluate : The value of m∠PQR when mPMQ⏜ = 212

Q: What is the equation for the following circle? center: (12, -1), radius: V209 (-12)2 +(y +1)? = 209…

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Q: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: Find the equation of the circle with center -2+i and radius 4 units. O (A) (x – 2)* + (y – 1)° = 4.…

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Q: Evaluate (r2 + y?)ds, C is the left half of the circle with radius 4 centered at (0,0) and is…

A: We calculate this by using concepts of line Integrals !

Q: Find the equation of the circle tangent to the line 3x – 4y + 6 = 0 at (2, 3) and passing through…

A: equation of circle

Q: What is the standard circle equation from the general circle equation: x2 +y? +8x=144+12y O K+42…

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Q: Use the arc length formula to find the length of the line segment y = 2-4x, 0<x<2. The length of the…

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Q: Find the DE of a family of circles with center at (1,-2). Hint: Equation of circle with center (h,…

A: We know that equation of circle with center h, k and radius r is given by, x-h2 + y-k2 = r2 We have…

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: Find the standard equation of the circle concentric with x? + y? +2x – 4y – 5 = 0, radius is 7.

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Q: Write the equation of the circle centered at (6, -2) and tangent to y = 1. O (x+ 6)° + (y – 2)² = O…

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Q: Find equation of the circle (in general form) that satisifes the given condition: With center on…

A: find the equation of circle using given information.

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 distance from the point (5,8) to the circle x+y2 + 2x + 6y +3 = 0

A: Please see the explanation below

Q: Use the arc length formula to find the length of the curve y = 5x – 1, -3 < x < 2. Check your answer…

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Q: What is the equation of the circle that has radius of 2 and centre at (-1,3)? A. (x+1) + (y – 3)² =…

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Q: Find the distance from the origin to the point (x, y).

A: Distance between Ax1, y1 and Bx2, y2 is, AB=x2-x12+y2-y12

Q: The standard equation of the circle with center (-1,-4) :and tangent to x-axis is اخترأحد الخیارات…

A: Stranded equations of the circle passing through center (h,k).

Q: What is the standard equation of a circle with radius 7 and is concentric (same center) with the…

A: Given:- x2 + y2  +2x-4y=5 To find:- Equation of circle concentric with given circle and radius 7

Q: Find an equation of the circle that satisfies the stated conditions.

A: We have to find the equation of the circle that satisfies the following conditions  * Tangent to…

Q: ㅠ Use Green's theorem to find: where C is the circle x² + y² = 4 going counter-clockwise. -8T […

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Q: -dz where C is the circle |z|=3. (z+ 2)* Evaluate

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Q: Evaluate (² + y2) ds, C is the top half of the circle with radius 2 centered at (0,0) and is…

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Q: What are the four main end points to the circle x2+y2-10x+8y+25=0 (show work)

A: Question is solved.

Q: Use the arc length formula to find the length of the curve y = 4x – 5, -1 < x < 3. Check your answer…

A: The arc length of the function y(x) over the interval a ≤x≤b is determined by the formula,

Q: Give the center and radius of this circle: x² + y? – 8x + 4y = –11 O Center (–4, 2); Radius =3 O…

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Q: What is the standard equation of the circle center at (3, 4) and tangent to the line x + 2y = 1? A.…

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Q: Use the arc length formula to find the length of the curve y 3x - 5, -1 <x< 2. Check your answer by…

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Q: Suppose that the circle with center (0, 0) and radius length r contains the point (a, b). Find the…

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Q: Consider the circle with center (h, k) and radius length r. If the circle contains the point (c, d),…

A: It is given that the centre of the circle is h,k and the radius of the circle is r. The circle is…

Q: Given the radius r = 12 and center (-7,10), find the standard equation of the circle. O (x+7)² +…

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Q: $ ydx – xdy where C is the circle of radius 3 with center at (13, 28)

A: We use Green's theorem to evaluate the given line integral