If the intercepts of the variable circle on the x- and yl-axis are 3
units and 6 units, respectively, then find the locus of the center of the
variable circle.
Text Solution
Verified by Experts
Let the equation of variable circle be `x^(2)+y^(2)+2gx+2fy+c=0` We have to find the locus of the centre C( -g,-f). According to the question, we have `2sqrt(g^(2)-c)=2` and `2 sqrt(f^(2)-c)=4` `:. g^(2)-c=1` ad `f^(2)-c=4` Eliminating c, we gt `f^(2)-g^(2)=3` or `(-f)^(2)-(-g)^(2)=3` Therefore, required locus is `y^(2)-x^(2)=3`.
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