Question

The line y=2-2x cuts the curve 3x^2-y^2=3 at the points A and B. Find the length of the line AB 20 points!

Answer 1

Step-by-step explanation:

put y=2-2x in the curve to find the intersection points A&B

$3 {x}^{2} - {(2 - 2x)}^{2} = 3$

$3 {x}^{2} - 4 - 4 {x }^{2} + 8x = 3$

${x}^{2} - 8x + 7 = 0$

x=1,7

at x=1

y=2-2(1)=0

A(1,0)

at x=7

y=2-2(7)= -12

B(2,-12)

Answer 2

Answer:

Step-by-step explanation:

put y=2-2x in the curve to find the intersection points of A & B

x= 1,7

at x = 1∴

y = 2 - 2 (1) = 0

∴A (1,0)

at x = 7

y= 2 - 2 (7) = -12

∴B (2,-12)

As a result: A=(1,0), B=(2,-12)