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Find the coordinates of the points of intersection of the parabola y=x^2 -ax and the line y=bx-ab

User UtsavShah
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Final answer:

To find the coordinates of the points of intersection between the parabola y = x² - ax and the line y = bx - ab, set the two equations equal to each other, solve for x using the quadratic formula, and substitute the x-values back into either equation to find the y-values.

Step-by-step explanation:

To find the coordinates of the points of intersection between the parabola y = x² - ax and the line y = bx - ab, we need to set the two equations equal to each other and solve for x.

Substituting y = x² - ax into y = bx - ab gives us x² - ax = bx - ab.

After rearranging the terms, we have a quadratic equation of the form ax² + (a-b)x - ab = 0. We can solve this equation using the quadratic formula to find the x-coordinates of the intersection points.

Once we have the x-coordinates, we can substitute them back into either equation to find the corresponding y-coordinates.

User Aminesrine
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