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Range of Quadratic Expression

x2+y2-6x-8y+9...

Question

$x^{2} + y^{2} - 6 x - 8 y + 9 = 0$ from $(- 2, 7) P A, P B$ are drawn. Find equation of $A B$ .

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Solution

We have
$x^{2} + y^{2} - 6 x - 8 y + 9 = 0$
$\Rightarrow - 2 x + 7 y + \frac{- 6 (x - 2)}{2} - \frac{- 8 (y + 7)}{2} + 9 = 0$
$\Rightarrow - 5 x + 3 y + 6 - 28 + 9 = 0$
$\Rightarrow - 5 x + 3 y - 13 = 0$

Therefore,
$e q u^{n} o f A B = 5 x - 3 y - 13 = 0$

Hence, this is the answer.

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