Circle 4 Question 5
5. The circle passing through $(1,-2)$ and touching the axis of $x$ at $(3,0)$ also passes through the point
(2013 Main)
(a) $(-5,2)$
(b) $(2,-5)$
(c) $(5,-2)$
(d) $(-2,5)$
Show Answer
Answer:
Correct Answer: 5. (c)
Solution:
- Let the equation of circle be $(x-3)^{2}+(y-0)^{2}+\lambda y=0$
As it passes through $(1,-2)$
$$ \begin{array}{ll} \therefore & (1-3)^{2}+(-2)^{2}+\lambda(-2)=0 \\ \Rightarrow & 4+4-2 \lambda=0 \Rightarrow \lambda=4 \end{array} $$
$\therefore$ Equation of circle is
$$ (x-3)^{2}+y^{2}+4 y=0 $$
By hit and trial method, we see that point $(5,-2)$ satisfies equation of circle.
