12. the centre and focus of the ellipse ( x+y -2 )2 /9 + ( x-y )2 / 16 = 1 , is
the locus of the point of intersection of the lines x/a +y/b = m & x/a - y/b = 1/m , where m is a parameter , is always :
(a)a circle
(b) a parabola
(c) a ellipse
(d) a hyperbola
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6 Answers
111for 2) the centre is (1,1).
(x+y-2√6)296 + (x-y√2)2162 = 1
or, X2(3√6)2 + Y2(√8)2 =1
u can get the centre, X=0 and Y=0
thus we get centre as (1,1).
1sorry , fr that
now the eq is correct
one more ques ......
the angle between the pair of tangents drawn to the ellipse , 3x2 + 2y2 = 5 , from the point ( 1,2 ) is :
111.
by solving, we get
x=a2 [m+1/m]
or, xa= 12 [m+1/m]
and , yb = 12 [m-1/m]
we know,
[m+1/m]2 - [m-1/m]2 = 4.m.1m
or, [m+1/m]2 - [m-1/m]2 = 4.
or, [ 12 (m+1/m) ]2 - [ 12 (m-1/m) ]2 = 1
or, x2a2 - y2b2 = 1.
thus it represents a hyperbola. :)
