Match each description to its equation. List I List II (A) Pair of lines through (2,1) parallel to the lines of 2x²-xy-y²+9x-3y+10=0. (P) x²-y²-24xy=0 (B) Pair of lines from the origin to the intersec

Question

Match each description to its equation.

List I	List II
(A) Pair of lines through (2,1) parallel to the lines of 2x²-xy-y²+9x-3y+10=0.	(P) x²-y²-24xy=0
(B) Pair of lines from the origin to the intersections of 3x+4y=5 and 2x²+3y²=5.	(Q) x²-(1/2)xy-(1/2)y²-(7/2)x+2y+5/2=0
(C) Ellipse: focus (2,1), directrix 2x-y+3=0, eccentricity 1/√2.	(R) x²+4xy+y²-32x-32y+154=0
(D) Hyperbola: focus (2,2), directrix x+y=9, eccentricity 2.	(S) 6x²+4xy+9y²-52x-14y+41=0

TestHub · Accepted Answer

(A) The directions factor as ( 2 x + y ) ( x − y ) , so the shifted lines satisfy ( 2 x + y − 5 ) ( x − y − 1 ) = 0 , namely (q). (B) Homogenize by 2 x 2 + 3 y 2 = 5 [( 3 x + 4 y ) /5 ] 2 , giving (p). (C) Equating squared focus distance to half the squared distance to 2 x − y + 3 = 0 gives (s). (D) Equating squared focus distance to four times the squared distance to x + y − 9 = 0 gives (r), not (p).

Mathematics - Coordinate Geometry Mixed Question with Solution | TestHub

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