Question

Find the point of intersection of the line x-y+2=0 and the circle 3x²+3y²-29x-19y +56=0.Also determine the length of the chord intercepted.​

Answer 1

Answer:

write the given line as

$y = x + 2$

put the value of y in the equation of the circle

$3 {x}^{2} + 3 {(x + 2)}^{2} - 29x - 19(x + 2) + 56 = 0$

which simplifies to

$6 {x}^{2} - 36x + 30 = 0$

or

${x}^{2} - 6x + 5 = 0$

which gives

$x = 1 \: and \: x = 5$

putting these values in the equation of the line we get

$y = 3 \: and \: y = 7$

thus the line intersects the given circle at the points (1,3) and (5,7).