square formed by the quadratic equations.

Question

Question:A Square is Formed By The Straight Lines $x^2-8 x+12 = 0$ And $ y^2-14y+45 = 0$. What are the coordinates?
How do I solve it? Providing a basic intiution will do the job.
Also the graphs of the equations have been referred to as straight but shouldn't they be parabolic?

Answer 1

Hint: Rewrite $-8=(-2+-6)$ and $-14=(-5+-9).$ Distribute the $x$ or $y$ (whichever is relevant) and factor by grouping and solve. This will then give you $4$ straight lines.

Alternately, you can solve the two quadratic equations by completing the square, or using the quadratic formula.

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In order to be parabolic, you'd need something like $y=x^2-8x+12$ or $x=y^2-14x+45.$