Help Math!! Please

Question

What are the solutions of the system

{(x-5)²+y²=16

{36y²-25x²=900

a. (5,4) and (1,0)

b. (5,4) and (6,0)

c. (0,5) and (6,0)

d. no solutions

Answer 1

The top equation is to a circle centered at (5, 0) with a radius of 4

The bottom equation is to a vertical hyperbola with vertices at (0, 5) and (0 -5)

The two do not intersect.

Answer 2

(x-5)² + y² = 16

36y²- 25x² = 900

Solve the 2nd equation for y²:

y² = (25/36) x² + 25

substitute for y² in the first equation:

(x-5)² + (25/36) x² + 25 = 16

expand the first term and simplify:

x2 - 10x +25 + 25/36)x2 + 9 = 0

(61/36)x2 - 10x + 34 = 0 ------the discriminant (b2 - 4ac) for this is negative, so the solution is imaginary.

Try it the other way----solve the first equation for y2, and then sub into the second equation