The coordinate of x is ( ? ).

Question

At what x-coordinate in the first quadrant does the line with equation y=x+3 intersect a circle with radius 2 sqrt 2 and center (0, 3)

Answer 1

Equation of circle is: (x - 0)² + (y - 3)² = (2√2)², or x² - (y - 3)² = 8.

Line y = x + 3. To get x-coordinate of intersection point we have: x² + (x + 3 - 3)² = 8; 2x² = 8; x² = 4, x = ±2.

Because 1st quadrant(x > 0) we have x = 2.