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).

a. she will receive a refund of $278.

step-by-step explanation:

u bout ugly as   a mf

step-by-step explanation: lol

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4