Let F=-yi+xj and let C be a curve consists of the line segment C₁ from (0,0) to (4,0) followed by the upper semicircle C₂ of the circle x² + y² = 4x, with counterclock- wise orientation.

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: i æ² + y? = 30 and (x + 1)? + (y – 1)² = 6 | ii (æ + 3)? + (y – 2)² = 9 and (x + 7)? + (y + 1)? = 4…

A: (i) The given circle is: x2+y2=30        ....1x+12+y-12=6       ....2

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: Consider the circle drawn in the xy-plane with center point (-5, 12). (x,y) (a) Determine the radius…

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Q: to the hyperbola the tangents. x² 16 9 = 1. Also, find the angle between

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Q: Find the equation of the circle if the circle is tangent to the line x + y = 1 at the point (0,1)…

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Q: Find an equation of the line which is tangent to the circle z + y - 4x + 6y – 12 = 0 at the point…

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Q: Sketch the second order spline that fits the end points PO (0,0), P2(9,4) and tangents intersection…

A: Here we need to sketch the second order spline that fits the end points P0 0,0, P2 9,4 and tangents…

Q: Find the number of common tangents to the circles x\power{2}+y\power{2}+2x+8y-23=0 and…

A: For x2+y2+2x+8y-23=0 ,C1≡(-1,-4),r=210for x2+y2-4x-10y+9=0,C2≡(2,5),r=25now C1C2=distance between…

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: If the straight line x - 2y + 1 = 0 intersects the circle x² + y² = 25 at points P and Q, then find…

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Q: Find the equation of the circle passing through (7,5) and (3,7) and with center on x-3y+3=0.

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Q: Find the distance from the point (4, 9) to the line y = 2x.

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