Question

Find all the points, if any, where the graph of 12x-5y=0 intersects (x+12)^2+(y-5)^2=169.

A. There are no points of intersection.

B. (0,0)

C. (4.5, 10.9)

D. (0,0) and (4.5, 10.9)

Answer 1

(0,0)

Explanation:

If you graph
`12x-5y=0` and
`(x+12)^2+(y-5)^2=169` along with the points (0,0) and (4.5, 10,9) you with see that the equations intersect at (0,0)

Answer 2

I: 12x-5y=0
II:(x+12)^2+(y-5)^2=169

with I:
12x=5y
x=(5/12)y
-> substitute x in II:
((5/12)y+12)^2+(y-5)^2=169
(25/144)y^2+10y+144+y^2-10y+25=169
(25/144)y^2+y^2+10y-10y+144+25=169
(25/144)y^2+y^2+144+25=169
(25/144)y^2+y^2+169=169
(25/144)y^2+y^2=0
y^2=0
y=0

insert into I:
12x=0
x=0

-> only intersection is at (0,0) = option B