Recent content by rajeshmarndi

That mean, even if the discriminant of the quadratic equation is positive, we can still get solution in complex form.

We have a circle (x^2 + y^2=2) and a parabola (x^2=y). We put x^2 = y in the circle equation and we get y^+y-2=0. We get two values of y as y=1 and y=-2. Y=1 gives us two intersection point i.e (1,1) and (-1,1). But y=-2 neither it lie on the circle nor on the parabola. The discriminant of the...

Let say we have two line ##a_1x+b_1y+c_1=0## and ##a_2x+b_2y+c_2=0##. Then pair of straight line equation is ##a_1a_2x^2+(a_1b_2+b_1a_2)xy+b_1b_2y^2+(a_1c_2+c_1a_2)x+(b_1c_2+c_1b_2)y+c_1c_2=0## i.e ##ax^2+2hxy+by^2+2gx+2fy+c=0## Now if we take ##a_1=0##, then the first line becomes...

While determining the condition for the pair of straight line equation ##ax^2+2hxy+by^2+2gx+2fy+c=0## or ##ax2+2(hy+g)x+(by^2+2fy+c)=0 ## (quadratic in x) ##x = \frac{-2(hy+g)}{2a} ± \frac{√((hy+g)^2-a(by^2+2fy+c))}{2a}## The terms inside square root need to be a perfect square and it is...

##w## becomes, ##w = [(s_1+t_1)x + (t_2-s_2)y] + i[(s_2+t_2)x + (s_1-t_1)y+r_2]=0## So the real terms of ##w## is ## [(s_1+t_1)x + (t_2-s_2)y]=0##

I want to know, given w= sz+tz*+r=0 Is w-w* = (s-t*)z + (t-s*)z* + r-r* = 0 also a complex straight line? [edit: r,s,t are non-zero complex number and z=x+iy (x,y ε R) ]

sz+tz*+r=0=say w so w* = s*z* + t*z + r*=0 Now , w+w* = (s+t*)z + (t+s*)z* + r+r* = 0 = p*z + pz* + k = 0...eq(1) ( k is a constant or twice real part of w) which is in complex straight line equation form i.e ab* + a*b + c = 0 ( a,b are complex number and c a real number. Now, again...

I was just curious to know, what current reading will it show, in such scenario.

Homework Statement If the current flow, in a branch of a circuit, is a function of say (√(x + 2)-2)/(x-2) (or any such that give an indeterminate form at a certain value) of an input source current x. What current will be flowing on that part of the circuit, when the function become...

For circles along x-axis. S1 = x^2 + y^2 + 2g1x + c1 = 0 S2 = x^2 + y^2 + 2g2x + c2 = 0 Family of circle of the above two circle. Center and radii as function of k. center = ( - ((g1+kg2)/(1+k)) , 0 ) and radius = √ ( [(g1+kg2)/(1+k)]^2 - [(c1+kc2)/(1+k)] ) From my example, it is. Center =...

Mentor note: Moved from a technical math section. What is the proof that the family of circles out of two non-intersecting circles, no two circles in that family intersect. Say S1 = x^2 + y^2 - 8x + 7 = 0 (i.e center at (4,0) and radius = 3 ) S2 = x^2 + y^2 - 24x + 135 = 0 ( i.e center...

Thanks a lot. I understand in infinity there is just no last room. If there is any last room, then the rooms are not infinite but instead consist of finite rooms. Since there are no last room, one can simply shift to the next room.

Then what does Hilbert actually want to show from his example.

In Hilbert infinity hotel, all the rooms were occupied. Then how did the occupant were able to shift to their adjoining room?? Here I understand, by full mean, ALL the infinite room has a corresponding occupant. I also understand some infinity number are greater because it can be proove when...

Little confused, this will only happen near a huge planet if the spaceship is large, because you mention tides on Earth due to moon and close to a black hole. [edit] If so what is the role of a large ship in which one can experience a force on a turn due to spacetime curvature.