class 11

Math

Co-ordinate Geometry

Conic Sections

PARAGRAPH $X$Let $S$be the circle in the $xy$-plane defined by the equation $x_{2}+y_{2}=4.$(For Ques. No 15 and 16)Let $E_{1}E_{2}$and $F_{1}F_{2}$be the chords of $S$passing through the point $P_{0}(1,1)$and parallel to the x-axis and the y-axis, respectively. Let $G_{1}G_{2}$be the chord of $S$passing through $P_{0}$and having slope $−1$. Let the tangents to $S$at $E_{1}$and $E_{2}$meet at $E_{3}$, the tangents to $S$at $F_{1}$and $F_{2}$meet at $F_{3}$, and the tangents to $S$at $G_{1}$and $G_{2}$meet at $G_{3}$. Then, the points $E_{3},F_{3}$and $G_{3}$lie on the curve$x+y=4$(b) $(x−4)_{2}+(y−4)_{2}=16$(c) $(x−4)(y−4)=4$(d) $xy=4$