Hi I have some questions, I'm not sure if I did them correctly..

1.

a.) The Cissoid of Diocles is a classical curve given by the equation

y^2 = x^3/2-x

Find the slope of the tangent line at the point (1,1)

b.) Consider the point (3,-4) on the circle centred at the origin. Find the equation of the tangent line at this point

Okay this is what I did

y^2 = x^3/2-x

= 2y y' = x^3/2-x

= y' = (1/2y)(x^3)/(2-x)

Sub the point (1,1) into the equation I get

m = 1/2

Then use the point slope equation I get y = 1/2x +1/2???

b.) x^2 + y^2 = 25

2x + 2y y' = 0

y' = -2x-2y

sub the points (3,-4) in I get m = 2

then use point slope equation I get y = 2x-10....

Someone taught me how to do the implicit differentiation for y', thats what I did above not sure If thats how you do it though...........help would be appreciated it

Also one more question

2. Find the constants c and K such that the functions f(x) = e^cx + k satisfies the differential equation

3f''(x) + 13f'(x) = 10f(x)

What I did was...

f(x) = e^cx + k

f'(x) = ce^cx

f''(x) = c^2e^cx

Sub these into the equation.

3(c^2e^cx) + 13(ce^cx) = 10(e^cx + k)

3c^2e^cx + 13ce^cx - 10e^cx = 10k

e^cx[3c^2 + 13c - 10] = 10k/e^cx

....then im not sure what to do anymore....

any help would be appreciated , thanks guys