solve all 3 of them for 50 points
Answers
Refer the attached picture.
Step-by-step explanation:
There is a point on this line that is the center of the circle we are trying to find. Let’s call it (x*, y*). We could also call it (x*, -(3/4)x* + 7/4).
So now we need to find what x* makes the distances from (x*, -(3/4)x* + 7/4) to (1, -2) and to (4, -3) the same.
d1 = radical( (1 - x*)^2 + (-2 - (-(3/4)x* + 7/4))^2 )
d2 = radical( (4 - x*)^2 + (-3 - (-(3/4)x* + 7/4))^2 )
( (1 - x*)^2 + (-2 - (-(3/4)x* + 7/4))^2 ) = ( (4 - x*)^2 + (-3 - (-(3/4)x* + 7/4))^2 )
( (1 - x*)^2 + (-2 + (3/4)x* - 7/4)^2 ) = ( (4 - x*)^2 + (-3 + (3/4)x* - 7/4)^2 )
( (1 - x*)^2 + ( (3/4)x* - 15/4)^2 ) = ( (4 - x*)^2 + ( (3/4)x* - 19/4)^2 )
1 - 2x* +x*^2 + (9/16)x*^2 - (90/16)x* + 225/16 = 16 -8x* + x*^2 + (9/16)x*^2 - (114/16)x* + 361/16
0 = 15 - 6x* - (24/16)x* + 136/16
(15/2)x* = 46/2
x* = 46/15.
So the center of the circle should be (46/15, -(3/4)(46/15) + 7/4),
and the radius should be radical( (1 - (46/15))^2 + (-2 - (-(3/4)(46/15) + 7/4))^2 ).