Match the following lists:

1.	Match the following lists:
Answer» (a) The equation of tangent at `((cos theta)//2,(sin theta)//3) "is" 2x cos theta+3ysin theta=1` Which is parallel to the given line `8x=9y`. Therefore, `cos theta=+-(4)/(5), sin =(+-3)/(5)` Hence, the points are (2/5,-1/5) and (-2/51/5). The distance between the points is `sqrt((16)/(25)+(4)/(25))=(2)/(sqrt(5))` Which is the given The given equation is `((x+1)^(2))/(9)+((y+2)^(2))/(25)=1` or `e^(2)=1-(9)/(25)=(16)/(25)or e=(4)/(5)` Hence, the foci, `S,S-=(1,-2+-4)-=S(-1,2) and S(-1.-6)` Required sum of distances `=2+6=8` (c) The equation of normal at `(3sos theta, 2 sin theta)` s `3xsec theta-2y "cosec" theta=5` whis is parallel to the given line `2x+y=1`. Therefore, `cos theta=+-(3)(5), sin theta=+-(4)/(5)` Hence, the points are `(-9/5,9/5) and (9/5,-8/5)` Required sum of the distances`=(16)/(5)` (d) Conider any point `(t,t+2), t in R` on the line `x-y+2=0` The chord of contact of the ellipse w.r.t. this point is `xt+2y(t+2)=2` or `(4y-2)+(x+2y)=0` This line passes trough the points of the intersection of lines `4y-2=0 and x+2y=0` `:. x=-1,y=1//2` Hence, the point is `(-1,1//2)` os 3.

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