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The centres of those circles which touch the circle, `x^2+y^2-8x-8y-4=0`, externally and also touch thex-axis, lieon :(1) a circle.(2) an ellipse which is not acircle.(3) a hyperbola.(4) a parabola.A. an ellipe which is not a circleB. a hyperbolaC. a parabolaD. a circle |
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Answer» Correct Answer - C Let C(h, k) be the centre of the circle touching x=axis and the circle `x^(2)+y^(2)-8x-8y-4=0` externally. The centre `C_(1)` of this circle has coordinates (4, 4) and its radius is 6. The circles with centres at C and `C_(1)` touch each other externally. `:." "C C_(1)=|k|+6` `rArr" "sqrt((h-4)^(2)+(k-4)^(4))=|k|+6` `rArr" "(h-k)^(2)+(k-4)^(2)=(|k|+6)^(2)` `rArr" "(h-4)^(2)-8k=12|k|+20` `rArr" "(h-k)^(2)=20k+20, if kgt0` `"or, "(h-k)^(2)=-4k+20, ifklt0` Hence, the locus of (h, k) is `(x-4)^(2)=20(y+1)or,(x-4)^(2)=-4(y-5)` which is a parabola. |
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