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Question 1040031: Given point A(0,2) on the parabola y^2=x+4. Points B & C also lie on the curve such that BC is perpendicular to AB. Find the slopes and equation of the lines AB and BC. Give the range of point C on the y-axis.
Thanks!
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Here is a plan for how to find the variable points B and C. I have not gone through the solution process to try this plan.
Sketch the parabola. It has points (0,2), (0,-2) and vertex (-4,0). Place a point B in the quadrant 1, and place point C in quadrant 2, with x-coordinate somewhat to the right of that of
B.
The parabola is of equation  .
Excuse the description of subscripted variable naming here, but point B would be y squared sub b minus 4, y sub b;
Point C would be y squared sub c minus 4, y sub c.
This would look good written on paper or in a conventional way.
You have A, B, C forming a right triangle allowing Pythagorean Theorem formula, and the slopes AB and BC, because they are perpendicular, are negative reciprocals of each other. This means you have a system of equations:
The parabola before any point labeling & drawing segments :
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