11are these multiple correct??
9) Number of points outside the hyperbola (x2/25) - (y2/36) =1 , from where two perpendicular tangents can be drawn to the hyperbola is(are)
a> 3 b> 2 c > 1 d>0
16) If a circle x2+y2=4 intersects a rectangular hyperbola at 4 points (0,±2) , (±2,0) , then the centre of the rectangular hyperbola is
a> (3,0) b> (0,-3) c> (0,0) d> (4,4)
19) One of the asymtotes of the curve 2x2+5xy+2y2+4x+5y=0 is
a> 2x+y+2=0 b>x+2y+2=0
c> 2x+y+1 =0 d> x+2y-1 = 0
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14 Answers
24vaise to main results yaad karne ke khilaaf hoon par coordinate mein iske bina kaam nahin chalta....
Q2 use the result::
OA2+OB2+OC2+OD2=4a2
where A,B,C,D are points of intersection and a is radiius of circle.........
and O =(h,k) is the centre of hyperbola
put the values and u will get h2+k2=0
which is satisfied by c only...........[1]
though u should try to prove this result........[1]
24Q1 ans=0
becoz hyperbola ke outside region se ek bhi tangent nahin ban sakti....[1]
62part 1)
see the tangent through a point (h,k)
is given by y=mx±√(a2m2-b2)
so (y-mx)2 = (a2m2-b2)
so the quadratic in m becomes
m2(x2-a2) - m(2xy) +b2+y2 = 0
product of roots has to be -1
so
y2+b2 = -1
x2-a2
thus, x2+y2-a2+b2=0
here, a<b so no solution.
adding more
playpowe..: pla explain why a<b and why there is no solution
Nishant: because sum of 2 squares cant be -ve
a=5, b=6
24sir main bhi to vahi kaha............
for Q3 pehle standard eqn bana.....
fir asymptote ki eqn likh de............x/a ± y/b =0[1]
1NISHANT bhaiya please explain WHY a<b and there is no solution... I THINK DATS DIRECTOR CIRCLE EQUATION [:)]
24always remeber tangents are always drawn from pt contained in convex region of curve
1den EUREKAH how many tangents can be drawn to a hyperbola if a>b plz explain .. will dat depends on parameter
62eureka I think the question only means from any point not on the hyperbola...
I understand that you are trying to do it with the definition of "Outside" and "Inside" points and you are correct too :)
but this works better for conics like circle and ellipse.
Otherwise, I will assume outside and inside as anypoints not on the curve.... (I know that the actual definition is something else!)
11hey play power change those > signs u have used for brackets in the options they were misleading particularly for the first question
24sir inside pts meant for which S1<0 and outside pts meant for which S1>0...........
i learnt geometric way of solving questions only from u.........[1][1]it becomes faster this way...