List - I List - II (P) Locus of centre of circles touching circles x 2 + y 2 − 4 x − 4 y = 0 internally and x 2 + y 2 − 6 x − 6 y + 17 = 0 externally (1) straight line (Q) The locus of the point ( 3 h

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List - I List - II (P) Locus of centre of circles touching circles x 2 + y 2 − 4 x − 4 y = 0 internally and x 2 + y 2 − 6 x − 6 y + 17 = 0 externally (1) straight line (Q) The locus of the point ( 3 h − 2 , 3 k ), where ( h , k ) lies on the circle x 2 + y 2 − 2 x − 4 y − 4 = 0 (2) Circle (R) Locus of centre of circles touching two circle x 2 + y 2 + 2 x = 0 and x 2 + y 2 − 6 x + 5 = 0 externally is (3) Ellipse (S) The extremities of a diagonal of a rectangle are ( 0 , 0 ) and (4,4). The locus of the extremities of the other diagonal is (4) Hyperbola

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(A) using 2nd definition of ellipse (B) Let α = 3 h − 2 , β = 3 k ⇒ 3 α + 2 ​ = h , 3 β ​ = k (C) 2nd defintion of hyperbola (D) circle with given diagonal as diameter

List - I	List - II
(P) Locus of centre of circles touching circles $x^{2} + y^{2} - 4 x - 4 y = 0$ internally and $x^{2} + y^{2} - 6 x - 6 y + 17 = 0$ externally	(1) straight line
(Q) The locus of the point ( $3 h - 2, 3 k$ ), where ( $h, k$ ) lies on the circle $x^{2} + y^{2} - 2 x - 4 y - 4 = 0$	(2) Circle
(R) Locus of centre of circles touching two circle $x^{2} + y^{2} + 2 x = 0$ and $x^{2} + y^{2} - 6 x + 5 = 0$ externally is	(3) Ellipse
(S) The extremities of a diagonal of a rectangle are $(0, 0)$ and (4,4). The locus of the extremities of the other diagonal is	(4) Hyperbola

Mathematics - Hyperbola Question with Solution | TestHub

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JEE Advanced 2027 (Class 12)