Maths · Points of intersection of a line and a circle with the centre at the origin
Equation of a straight line meeting the circle in two points each point at a dis
Equation of a straight line meeting the circle \( x^{2}+y^{2}=100 \) in two points each point at a distance of 4 from the point (8,6) on the circle is
- A. \( 4 x+3 y-50=0 \)
- B. \( 4 x+3 y-100=0 \)
- C. \( 4 x+3 y-46=0 \)
- D. none of these
Step-by-step solution
The point (8,6) lies on the circle x^2+y^2=100. The required line intersects the given circle at two points that are each 4 units away from (8,6). These two points also lie on a circle centered at (8,6) with radius 4: (x-8)^2+(y-6)^2=16. The line is the common chord of the two circles. Subtracting the equations yields -16x-12y+184=0, which simplifies to 4x+3y-46=0.