If C is the unit circle centered at the origin and oriented counterclockwise, then Lo -y - x) dx + (x³ +x+ y)dy =.

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

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Q: Evaluate ∫ C ( 2 + x^2 y ) d s , where C is the upper half of the unit circle.

A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

Q: 2. Evaluateſ. a+ (z+30:) dz along C which is the circle |z + 3i| = 3, counterclockwise. %3D (z+3i)

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Q: Evaluate 12x-7 dz where (2213) (2-1)² Cis the circle Z = 2

A: Approach to solving the question:  Detailed explanation:

Q: point

A: Please refer to the image below

Q: Find the image of (4,-1) obtained by translating 4 units up, followed by a reflection over the…

A: We have to find the image of (4,-1) obtained by translating 4 unit up and then reflection over y…

Q: Find the angle at which the circle  x2+y2 +x+y=0 and x2 +y2 + x-y=0 intersect.

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Q: Are the points H and L collinear? U S E H.

A: Collinear means the points which lie on the same line.  From the image, we see that H and L lie on a…

Q: Evaluate (x² - y²) dx + (x² + y²) dy, where C is the circle x² + y² = 9 oriented counterclockwise.…

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Q: Evaluate (x+ y)ds, where C is the top half of the circle x² + y² = 4, oriented counterclockwise.

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Q: Find the angle at which the circles x2 +y2 +x+y=0 and x2 +y2 +x-y=0 intersect.

A: The angle of intersection of the two circles is given by cosθ=r12+r22-C1C22r1r2where r1 and r2 are…

Q: Q6. Evaluate (2yx² - 4x)ds, where C is the lower half of the circle centered at the origin of radius…

A: check belowExplanation:Step 1:Step 2:Step 3: Step 4:

Q: Let P(t) be the point on the unit circle U that corresponds to t. If P(t) has the given rectangular…

A: a. -1213,-513 is in quadrant III.Adding pi to the angle rotates it 180 degrees to the quadrant I…

Q: Find the center and radius of the circle x2+y2-2x-18y+1=0

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Q: 10. Find the equation of the circle that has a center at (3, 3) and is tangent to the y- axis? a.…

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Q: Find the angle between y=5x2-3 and 3xy-9x2-x

A: Given y=5x2-3 --- Eq 1 and 3xy=9x2-x      --- Eq 2We know that angle between y1=k1x+b1 and y2=k2x+b2…