A circle touches a given straight line and cutsoff a constant length 2d from another straight line perpendicular to the first straight line. The locus of the centre of the circle is
A
hyperbola
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B
circle
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C
parabola
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D
Pair of perpendicular lines
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Solution
The correct option is A hyperbola let the equation of the circle x2+y2+2gx+2fy+c=0 It is touching x axis.The equation of the circle becomes x2+2gx+c=0 Since , it is touching x axis.D=0 g2=c Intercept made on y axis=2√f2−c 2√f2−c=2d f2−c=d2 f2−g2=d2 y2−x2=d2