Circle: (a) r + y2 + 2r - 3y + 13 = 0 at (1, -2); (6) 2r + 2y2 - 3x + 4y - 32 = 0 at (2, 3); (c) r2 + y2 - 2x - y - 15 = 0 at (-1,-3); (d) 3rd + 3y2 - 8x - 6y - 61 = 0 at (4, 5).8. find the equations of the normal to thefollowing circle at the given points on thecurve: (a) r2 + y2 + 3x + 5y - 18 = 0 at (1, 2); (6) r2 + y2 - 4x + 2y - 4 = 0 at (2, 4); (c) 4x2 + 4y2 – 5x - 6y - 19 = 0 at (3, 1); (d) 2x + 2y2 - x - 3y - 41 = 0 at (2,-5).

step-by-step explanation:

1. the cylinder is a. 54

2.   a.108 /

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

yes

step-by-step explanation:

yes