Find point P on y = x^2 so sum of x-,y-coords of P is 2

[caseygaspar]

Okay I have another one...

Find a point P on the curve y=x^2 so that the sum of the x- and y- coordinates of P is 2. Also find a different Point Q satisfying the same conditions.

Yeah this one I don't even know how to start.

I know Im going to ace this test because of all the help I am receiving. THanks guys. you guys are a big help!

 

[PAULK]

Re: Points on a parabola.

Okay I have another one...

Find a point P on the curve y=x^2 so that the sum of the x- and y- coordinates of P is 2. Also find a different Point Q satisfying the same conditions.

Yeah this one I don't even know how to start.

I know Im going to ace this test because of all the help I am receiving. THanks guys. you guys are a big help!

Start by translating: "the sum of the x- and y- coordinates of P is 2" into algebraic notation:

the sum of the x- and y- coordinates of P is 2
the sum of the x- and y- coordinates of P = 2
+ x- and y- coordinates of P = 2
x + y = 2
y = 2 - x can be substituted into y = x^2.

Now you are on your way.

 

[stapel]

Find a point P on the curve y=x^2 so that the sum of the x- and y- coordinates of P is 2. Also find a different Point Q satisfying the same conditions.

Since you're restricted to the curve y = x[sup:qlng0t9v]2[/sup:qlng0t9v], then all the points you care about are of the form (x, x[sup:qlng0t9v]2[/sup:qlng0t9v]). The sum of the coordinates of the point has to be 2, so add the x-variable and the y-expression (in terms of x), set the sum equal to "2", and solve the resulting quadratic.

You should get two solutions. P will be one; Q will be the other. :wink:

Eliz.