Question

The coordinates of the fixed point of the chord cut off by $2x-5y+18=0$ by the circle $x^2+y^2-6x+2y-54=0$ are

• A. $(1,4)$
• B. $(2,4)$
• C. $(4,1)$
• D. $(1,1)$

Answer 1

Answer: (A)

$(1,4)$

The point should satisfy the equation $2x-5y+18=0$
Hence
Substituting $(1,4)$ we get $-18+18=0$ ...(i)
Substituting $(2,4)$ we get $-16+18=-2\ne 0$ ...(ii)
Substituting $(4,1)$ we get $3+18=21\ne 0$ ...(iii)
Substituting $(1,1)$ we get $-3+18=15\ne 0$ ...(iv)
Hence only possible answer is $i$ that is option A.