2. Let C₁ denote the positively oriented boundary of the square whose sides lie along the lines x = ±1, y = 1 and let C₂ be the positively oriented circle |z| = 4 (Fig. 63). With the aid of the corollary in Sec. 49, point out why when (a) f(z) = 1 3z²+1 C₁ C₂ Lo f(z) dz= = √₂ (b) f(z) = 4 2+2 sin(z/2) f(z) dz (c) f(z) = N 120

Q: %3D 1. Write the image points for T-5,3>(ADEF) =ADIE¡FI. D'( E'C

A: In the given figure, D(2,1), E(5,1), F(4,-2). T-5,3(∆DEF)=∆D'E'F' The translation T-5,3 moves all…

Q: If the straight line x - 2y + 1 = 0 intersects the circle x² + y² of the point of intersection of…

A: Let R(h,k) be the point of intersection of the tangents drawn at P and Q to the given circle.Then PQ…

Q: (b) Sketch the graph of the function y = 1+ /16 – x²2 for -4 < x < 4. Hint: x2 + y? = 16 is the…

A: Consider the equation of the circle The graph can be plotted for the circle as

Q: The line tangent to the circle expressed as x² + y² = 5 at the point (x,x)= (1,2). Find the…

A: We will find out the required equation of tangent line.

Q: 2. The circle, if the center of the circle of radius 3 lies on the line x + 2y = 4 and it is tangent…

A:

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

A:

Q: If the radical axis of the circles x² + y² + 2 gx + 2 fy+c= 0 and 2x² + 2y² +3x+8y +2c=0 touches the…

A: The radical axis of the given circles             x2+y2+2gx+2fy+c=0and      x2+y2+(3/2)x+4y+c=0 is…

Q: 3. The distance between two distinct points (x1, y1) and (x2, y2) is given by the formula

A: Given: Points x1, y1 and x2, y2

Q: 4. What is the equation of a circle with radius 3 and center (3, 0)? A. x2 + y2 – 6x = 0 B. x2 + y?…

A: equation of the circle with radius 3 and center (3, 0) :(x-3)2+(y-0)2 = 32

Q: 2. A curve is defined by f(x) = a√√x+b, where a and b are constants. the point (4, 6), determine the…

A:

Q: Y = , cx. y) = (9,5) X-8 会? Jengent line -? at (9,5)

A: Explanation of the answer is as follows

Q: If the straight line x-2y+1=0 intersects the circle x\power{2}+y\power{2}=25 at points P and Q,then…

A: we need to find the coordinates of the point of intersection of the tangents drawn at P and Q to the…

Q: a) Given that straight line y + x=2 is tangent to the curve y =x² – 6x + q. Find value q.

A: Given,  y+x=2⇒y=-x+2

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

A:

Q: 8. Is the point (2, –7) on the circle defined by (x + 6) + (y + 1) = 100?

A: Given the equation of a circle, x+62+(y+1)2=100                   ...(1)

Q: Prove that the equation of any tangent to the circle x\power{2}+y\power{2}-2x+4y-4=0 is of the from…

A:

Q: What is the equation of the circle that has radius of 8 and centre at(-3, 4)? A. (x +3)2 + (y – 4)?…

A:

Q: 16xydx- 24ydy = -8x²dy %3D

A: The given differential equation can be written as:16xy−24yy' =−8x2y' An ODE Mx, y+Nx, yy'=0 is in…

Q: 3) Find the distance from ( − 11 , − 8 ) to ( 1 , − 13 ).

A:

Q: Find the distance from the point (-3, 2, -4) to the plane 5x + 5y - 4x = 3.

A:

Q: Find the shortest distance from the point (2,1) to the curve y = 1+√x.

A: