Hyperbola Definition and 107 Threads

hi i got this equation y= x^2 - 2x + 1 / X^2 -x - 2 how do i sketch this finding all intercepts, and asymptotes with a gfx calculator? Please check if the steps i did below is right what i did i factorised the equation so i got y= (x-1)^2 / (x+1)(x-2) ASYMPTOTES the bottom line...

:cry: \frac {(x-1)^2} {9} - \frac {(y+2)^2} {25} = 1 I think this is a vertical hyperbola with center (1,-2) a=5 b=3 Transversal length=10 Conjugate length =6 Vertex (1,-7) and (1,3) Foci (1,sqrt(34)-2) and (1,-sqrt(34)-2) Asymptotes y+2=5/3(x-1) and y+2=-5/3 (x-1) I don't...

Find the equation of the hyperbola with centre at the origin and sketch the graph. e. tranverse axis is on the y-axis and passes through the points R(4, 6) and S(1, -3) How would I find a and b? I plugged in the coordinates in \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 and came up with two...

What is a conjugate hyperbola? I'm asked to find the equation of the conjugate hyperbola if the asymptotes are y = +/- 2x. Would it be \frac{x^2}{1} + \frac{y^2}{4} = 1 or \frac{x^2}{1} + \frac{y^2}{4} = -1?

Find the area of the region bounded by the hyperbola 9x^2-4y^2 = 36 and the line x = 3. I'm thinking that I have to integrate for x, so I'll have the sum of twice the area from 2 to 3. The function will be + \sqrt {\frac {9x^2-36}{4}} hence, the integral will be 2\int_2^3 {\sqrt {\frac...

|F||D|=1 is the simplest form of the law of lever in equilibrium. If |F|=|x-y| and |D|=x+y then |x^2-y^2|=1 is an real hyperbola. In this case the interaction is repulsive. If |F|=x-iy and |D|=x+iy then x^2+y^2=1 is an real ellipse or imaginary hyperbola. In this case the interaction is...

Hey everyone, I was having trouble with this question. The graph of 1/x is a hyperbola, but it's equation does not fit the form (x-h)/(a^2) - (y-k)/(b^2) = 1. Rotate 1/x using polar coordinates, change it back into cartesian coordinates, and write the equation in standard hyberbola notation...