Question

a line through (2, 1) meets the curve x²-2x-y=3 at A(-2,5) and at B. FIND THE COORDINATES OF B
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Answer 1

Answer:

(3,0)

Step-by-step explanation:

We know the line will Pss through

(-2,5) and (2,1) so

let find the slope

$\frac{1 - 5}{2 - ( - 2)} = \frac{ - 4}{4} = - 1$

So the slope is -1.

We know it passes through 2,1 so use point slope to find b.

$y - 1 = - 1(x - 2)$

$y - 1 = - x + 2$

$y = - x + 3$

Set that equal to

${x}^{2} - 2x - y = 3$

${x}^{2} - 2x - 3 = y$

${x}^{2} - 2x - 3 = - x + 3$

${x}^{2} - x - 6 = 0$

$(x - 3)(x + 2) = 0$

$x = 3$

Point (3,0).