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Athul Vincent
Subject: Maths
, asked on 12/12/17
Derive an equation for the point of intersection of two tangents drawn to a parabola
Answer
1
Athul Vincent
Subject: Maths
, asked on 12/12/17
Equation of the line of lactus rectum of the curve xy=4 is
Answer
1
Athul Vincent
Subject: Maths
, asked on 12/12/17
The curves y
^{2}
= 4a(x+2) (a>0) and x
^{2}
+ y
^{2}
= 4 intersect each other in points A and B, then value of 'a' [or which area of the region bounded by the parabola and chord AB is maximum is given by
Answer
1
Athul Vincent
Subject: Maths
, asked on 12/12/17
How is it that lx + my = 1 has been rewritten as shown in the image. Please provide examples to illustrate similar rearrangement
Answer
1
Athul Vincent
Subject: Maths
, asked on 12/12/17
"For a given parabola and a given point (h, k), this cubic in m has three roots say m1, m2, m3 i.e. from (h, k) three normals can be drawn to the parabola whose slopes are m1, m2, m3. For this cubic, we have m
_{1}
+ m
_{2}
+ m
_{3}
= 0, m
_{1}
m
_{2}
+ m
_{2}
m
_{3}
_{}
+ m
_{3}
m
_{1}
= (2a – h)/a and m
_{1}
m
_{2}
m
_{3}
= –k/a."
Prove :
1. m1 m2 + m2 m3 + m3 m1 = (2a – h)/a
2.m1 m2 m3 = –k/a.
Answer
1
Pratik Kadam
Subject: Maths
, asked on 12/12/17
Q.81
$Acommon\mathrm{tan}genttotheconics{x}^{2}=6yand2{x}^{2}-4{y}^{2}=9,\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}A.x+y=1\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}B.x-y=1\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}C.x+y=\frac{9}{2}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}D.x-y=\frac{3}{2}$
Answer
1
Athul Vincent
Subject: Maths
, asked on 12/12/17
"For a given?parabola?and a given point (h, k), this cubic in m has three roots say m1, m2, m3?i.e. from (h, k) three?normals?can be drawn to the parabola whose slopes are m1, m2, m3. For this cubic, we have m1?+ m2?+ m3?= 0, m1?m2?+ m2?m3?+ m3?m1?= (2a ? h)/a and m1?m2?m3?= ?k/a." 1. Derive m1?m2?+ m2?m3?+ m3?m1?= (2a ? h)/a.2. Derive m1m2m3=-k/a
Answer
1
Athul Vincent
Subject: Maths
, asked on 12/12/17
As you can see in the picture , two equations have been combined using the symbol lambda 1.Using what logic has that been done?2. Can we use the same logic too solve all types of equations?
Answer
1
Ritwik Kumar
Subject: Maths
, asked on 11/12/17
Bye friends it's my last day on meritnation . I'll miss u all it was a wonderful pleasure to study with u all great friends who were very responsive to my doubts that I asked . I made a lot of friends here especially Nikita Nag from Bhuvneshwar I couldn't talk to her much because my laptop was stolen and then on I operated my account on my mobile phone . Thank you and bye once again.
Answer
1
Athul Vincent
Subject: Maths
, asked on 11/12/17
"Let y^2= 4ax be the equation of a parabola and (x1, y1) an external point P. Then, equation of the tangents is given by?
SS1= T^2,where S = y^2-4ax, S1= y1^2- 4ax1, T = yy1 2a(x-x1)"?
How is the equation tangent given by SS1=T^2 ?
Answer
1
Athul Vincent
Subject: Maths
, asked on 11/12/17
Derive an equatiom for the tangent to a point t on a parabola(ty=x+at^2)
Answer
1
Vibhansh Agarwal
Subject: Maths
, asked on 11/12/17
Q. A tangent to the hyperbola
$\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1$
meets its asymptotes at P and Q. If C is its centre, prove that CP. CQ = a
^{2}
+ b
^{2}
.
Answer
1
Athul Vincent
Subject: Maths
, asked on 11/12/17
Derive a formula for the angle between two tangents(for an ellipse)
Answer
1
Pragya Priyadarshini
Subject: Maths
, asked on 10/12/17
an isosceles triangle is inscribed in the parabola y^2=4ax with its base as the line joining the vertex of the parabola and positive end of the latus rectum of the parabola, if (at^2, 2at) is the vertex then 1)2t^2-8t+5=0 2)2t^2+8t-5=0 3)2t^2+8t+5=0 4)2t^2-8t-5=0
Answer
1
Smridhi Verma
Subject: Maths
, asked on 10/12/17
Find the distance between the directrix of the ellipse x^2 +36 + y^2 +20=1
Answer
1
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What are you looking for?

^{2}= 4a(x+2) (a>0) and x^{2}+ y^{2}= 4 intersect each other in points A and B, then value of 'a' [or which area of the region bounded by the parabola and chord AB is maximum is given by_{1}+ m_{2}+ m_{3}= 0, m_{1}m_{2}+ m_{2}m_{3}_{}+ m_{3}m_{1}= (2a – h)/a and m_{1}m_{2}m_{3}= –k/a."Prove :

1. m1 m2 + m2 m3 + m3 m1 = (2a – h)/a

2.m1 m2 m3 = –k/a.

$Acommon\mathrm{tan}genttotheconics{x}^{2}=6yand2{x}^{2}-4{y}^{2}=9,\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}A.x+y=1\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}B.x-y=1\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}C.x+y=\frac{9}{2}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}D.x-y=\frac{3}{2}$

SS1= T^2,where S = y^2-4ax, S1= y1^2- 4ax1, T = yy1 2a(x-x1)"?

How is the equation tangent given by SS1=T^2 ?

^{2}+ b^{2}.