Help with line equations?

First question





now we have to replace the y of curve by the y of line, therefore









we can multiply each member by



Now we have to find the roots of this funtion



Sum and produc or Bhaskara

Then we find two axis



now we replace this values to find the Y, we can replace in curve or line equation, I'll prefer to replace it in line equation.















Therefore


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The second question give to us







We just have to replace the value then we'll get a linear system.

point 1



point 2



then our linear system will be



I'll multiply the second line by -1 and I'll add to first one







therefore we can replace the value of a, at second line







then our function will be



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The third one, we have





This resolution will be the same of our first question.

Let's replace the y of curve by the y of line





therefore

 

now we have to find the roots of this function.



put x in evidence





then

















our points will be



I hope you enjoy it ;)

It would be 18 cm