Find a set of parametric equations that represents the graph of y=1−x2 using each of the following parameters. a) t=x b) The slope m=dydx at the point (x, y)

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Find a set of parametric equations that represents the graph of  y=1−x2  using each of the following parameters.   a) t=x  b) The slope m=dydx at the point (x, y)

Robert Harris · Accepted Answer

Step 1 Given: y=1−x2 To find: Find a set of parametric equations that represents the above graph using each of the following parameters a) t=x b) The slope m=dydx at the point (x, y) Step 2 Explanation: Rewrite the given expression, 1) y=1−x2 a) As we have to find a set of parametric equations in the parameter t=x, we get, y=1−(t)2 y=1−t2 b) As we have to find the slope, so differentiating the above equation w.r.t. x, we get, dydx=0−2x dydx∣(x, y)=−2x So, the slope of the above equation at point (x,y) is −2x. Hence, a set of parametric equations in the parameter t=x is y=1−t2 and the slope of the function y=1−x2 at point (x, y) is -2x.

Find a set of parametric equations that represents the graph

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