Circle 3 Question 19
19. If a circle passes through the points of intersection of the coordinate axes with the lines $\lambda x-y+1=0$ and $x-2 y+3=0$, then the value of $\lambda$ is … .
$(1991,2 M)$
Analytical & Descriptive Questions
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Answer:
Correct Answer: 19. $\lambda=2$ or $-\frac{1}{2}$
Solution:
- Since, the point of intersection of the coordinate axes with the line $\lambda x-y+1=0$ and $x-2 y+3=0$ forms the circle.
$$ \therefore \quad(\lambda x-y+1)(x-2 y+3)=0 $$
represents a circle, if coefficient of $x^{2}=$ coefficient of $y^{2}$ and coefficient of $x y=0$
$$ \begin{array}{llll} \Rightarrow & \lambda=2 & \text { or } & -2 \lambda-1=0 \\ \Rightarrow & \lambda=2 & \text { or } & \lambda=-\frac{1}{2} \end{array} $$
