JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q79

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MathematicsSingle correct+4 / -1Question 79 of 90

The centres of those circles which touch the circle, $x^2+y^2-8x-8y-4=0$ , externally and also touch the $x$ -axis, lie on :

a circle.

an ellipse which is not a circle.

a hyperbola.

a parabola.

Answer and worked solution

Official answer: D

The given circle has centre (4, 4) and radius 6. A circle with centre (h, k), k > 0, touching the x-axis has radius k, and external contact gives $(h-4)^2+(k-4)^2=(k+6)^2$ , i.e. $(h-4)^2=20(k+1)$ : a parabola.

Topics:Parabola Family of circles

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JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 79