If m is the slope of the common tangent of the parabola y2 = 16x and the circle x2 + y2 = 8, then m2 is equal to :
Question
If m is the slope of the common tangent of the parabola y2 = 16x and the circle x2 + y2 = 8, then m2 is equal to :
Solution
To find the slope of the common tangent of the parabola y^2 = 16x and the circle x^2 + y^2 = 8, we need to find the point of tangency between the two curves.
First, let's find the point of tangency by solving the system of equations formed by the parabola and the circle.
Substituting y^2 = 16x into the equation of the circle, we get: x^2 + (16x) = 8 x^2 + 16x - 8 = 0
Solving this quadratic equation, we find two possible values for x. Let's call them x1 and x2.
Once we have the x-values, we can substitute them back into the equation of the parabola to find the corresponding y-values. Let's call them y1 and y2.
Now that we have the coordinates of the two possible points of tangency, we can find the slope of the line passing through these points.
Using the formula for slope, m = (y2 - y1) / (x2 - x1), we can calculate the slope of the line passing through the two points.
Finally, to find m^2, we simply square the value of m.
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