Question

show that the line x+y-5=0 touches the circle x2+y2-2x-4y+3=0. find the point of contact

Answer 1

$y = 5 - x$
using this in circle equation
${x}^{2} + {(5 - x)}^{2} - 4(5 - x) + 3 = 0$
simplifying we get
${x}^{2} - 4x + 4 = 0$
$x = 2$
$y = 3$
on solving these two equations we get
only one point in common.
hence the given line will not be a secant .

Therefore the line is a tangent to the circle.
point of contact is (2,3)

Answer 2

Answer:

(2,3) = (x, y)

here is ur Ans