Circle 1 Question 14
14. The lines $3 x-4 y+4=0$ and $6 x-8 y-7=0$ tangents to the same circle. The radius of this circle is…
(1984, 2M)
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Answer:
Correct Answer: 14. $x^{2}+y^{2}+2 a x+2 p y-\left(b^{2}+q^{2}\right)=0$, radius $=\sqrt{a^{2}+p^{2}+b^{2}+q^{2}}$
Solution:
- Since, $3 x-4 y+4=0$ and $3 x-4 y-\frac{7}{2}=0$ are two parallel tangents. Thus, distance between them is diameter of circle
$$ \begin{array}{rlrl} \Rightarrow & & \text { Diameter } & =\frac{\left|4+\frac{7}{2}\right|}{\sqrt{3^{2}+4^{2}}}=\frac{15}{2.5}=\frac{3}{2} \\ \text { and } & \text { radius } & =\frac{3}{4} \end{array} $$
