Match each locus to its type. Column I: (A) Centres of variable circles internally tangent to x 2 + y 2 − 4 x − 4 y = 0 and externally tangent to x 2 + y 2 − 6 x − 6 y + 17 = 0 . (B) Locus of ( 3 h −

Question

Match each locus to its type. Column I: (A) Centres of variable circles internally tangent to $x^{2} + y^{2} - 4 x - 4 y = 0$ and externally tangent to $x^{2} + y^{2} - 6 x - 6 y + 17 = 0$ . (B) Locus of $(3 h - 2, 3 k)$ where $(h, k)$ lies on $x^{2} + y^{2} - 2 x - 4 y - 4 = 0$ . (C) Centres of variable circles externally tangent to $x^{2} + y^{2} + 2 x = 0$ and $x^{2} + y^{2} - 6 x + 5 = 0$ . (D) The other vertex of a rectangle whose diagonal endpoints are (0,0) and (4,4).

Column I	Column II
(A) Centres of circles internally tangent to x²+y²−4x−4y=0 and externally tangent to x²+y²−6x−6y+17=0	(p) Straight line
(B) Locus of (3h−2,3k) for (h,k) on x²+y²−2x−4y−4=0	(q) Circle
(C) Centres externally tangent to x²+y²+2x=0 and x²+y²−6x+5=0	(r) Ellipse
(D) Other vertex of rectangle with diagonal (0,0) to (4,4)	(s) Part of hyperbola

TestHub · Accepted Answer

A: the sum of centre distances to the two fixed centres is constant, an ellipse or arc subject to the contact restrictions. B: translation and uniform dilation of a circle give a circle. C: the difference of distances to the two fixed centres is constant, a branch of a hyperbola. D: the right-angle condition gives a circle with diameter from ( 0 , 0 ) to (4, 4); exclude its endpoints if the rectangle must be nondegenerate.

Mathematics - Circle Question with Solution | TestHub

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