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This will help you find what your looking for
You'll need to use differentiation (specifically, implicit differentiation) here.
If x^2 = 4(y+6), differentiating both sides with respect to time t produces the following:
2x (dx/dt) = 4([dy/dt]) (note that (d/dt) 6 = 0)
We need to solve for (dx/dt). Substitute 8 for x (y does not appear in this latest equation, so we do nothing with y=10). Substitute the given 5 units/sec for dy/dt:
2(8)(dx/dt) = 4(5)(units/sec)
Solving for dx/dt, dx/dt = [20 units/sec]/16, or 5/4 units/sec, or 1.25 units/sec.
Answer:
(x + 2/3)^2 + (y + 3/4)^2 = 5^2 (or 25).
Step-by-step explanation:
Start with the general equation of a circle with center at (h, k) and radius r:
(x - h)^2 + (y - k)^2 = r^2
Substitute -2/3 for h and -3/4 for k, and also 5 for r:
(x - [-2/3])^2 + (y - [-3/4])^2 = 5^2, or
(x + 2/3)^2 + (y + 3/4)^2 = 5^2 (or 25).
