Multiple choice

If two circles, each of radius 5 units, touch each other at (1, 2) and the equation of their common tangent is 4x + 3y = 10, then the equation of the circle, a portion of which lies in all the quadrants, is

  1. x2 + y2 – 10x – 10y + 25 = 0

  2. x2 + y2 + 6x + 2y – 15 = 0

  3. x2 + y2 + 2x + 6y – 15 = 0

  4. x2 + y2 + 10x + 10y + 25 = 0

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The center of the circles must lie on a line perpendicular to the tangent 4x+3y=10, passing through (1,2). The line is 3x-4y+c=0. 3(1)-4(2)+c=0 => c=5. The centers are at distance 5 from (1,2) along this line. The equations provided in the options can be checked for the center and radius.