How Can I Solve These Two Calculus Problems on Parabolas and Tangents?

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To solve the first problem, the change in y from (1,1) to (x,x^2) is calculated as x^2 - 1, while the change in x is x - 1, leading to the conclusion that (change in y)/(change in x) equals x + 1. For the second problem, the tangent line to the circle at (-2, 6) can be found by first determining the slope of the radius from the center (1, 2) to the point (-2, 6). The slope of the radius is calculated, and the slope of the tangent line is the negative reciprocal of this slope. Once the slope of the tangent line is known, the equation can be derived using the point-slope form. Understanding these concepts will help in solving both calculus problems effectively.
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I'm having a little trouble with 2 problems because the day that they went over the problems i was out of school and my freakin teachers is never there after school to help me.

1) A particle moves along the parabola y = x^2 from the point (1,1) to the point (x,y) Show that (change in)y/(change in)x = x +1

2) Consider a circle of a radius 5, centered at (1,2). Find an equation of the line tangent to the circle at the point (-2, 6). Describe th procedure that you used to get your answer.
 
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The particle will move from (1, 1) to (x, x2) since y= x2.

Okay, y has changed from 1 to x2. What is the "change in y"? How much does y change?

x has changed from 1 to x. What is the "change in x"? How much does x change?

If you can answer those, just divide!

There are two ways I can think of two answer (2). One of them involves writing the equation of the circle and using "implicit differentiation" to find the slope of the tangent line- you may not be ready for that.

The other is- find the slope of the line from (1,2) to (-2, 6), a radius of the circle. The tangent line at (-2, 6) must be perpendicular to that radius. Do you know how to find the slope of a line perpendicular to a given line (and you know the slope of that line)? After you know the slope of the tangent line and that it goes through (-2, 6) it should be easy to find the equation.
 
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