Why is this statement true? Circle algebra

Elliottbissell

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Im self teaching A-level maths and im struggling on a question. i was given the equation of a circle and an equation of a tangent. i have re-arranged the equation to a point but couldn't figure out how to go further and i used the answer sheet to see which step i should take but it gives a statement that i don't understand why it is true. just taking the statement as it is i can work out the rest of the equation but i feel i need to understand how to use it to make the studying useful. the equation, my progress as well as the statement are attached.

Thanks in advance,

Elliott
 

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Im self teaching A-level maths and im struggling on a question. i was given the equation of a circle and an equation of a tangent. i have re-arranged the equation to a point but couldn't figure out how to go further and i used the answer sheet to see which step i should take but it gives a statement that i don't understand why it is true. just taking the statement as it is i can work out the rest of the equation but i feel i need to understand how to use it to make the studying useful. the equation, my progress as well as the statement are attached.

Thanks in advance,

Elliott
attachment.php


Hint: discriminant of a quadratic equation.
 
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