Question

mid point question

Answer 1

(x1+x2/2,y1+y2/2) Is that it?

Answer 2

no one sec

Answer 3

Suppose the tangent line at a point P on the hyperbola xy = 3, cuts the
x-axis at point A and the y-axis at point B.

Answer 4

Show that P is the mid-point of the line segment AB.

Answer 5

first find the equation of the tangent line, it doesnt matter if there are extra variables, then prove that 1/2 the x coordinate of A and 1/2 the y coordinate of B are the same as the x and y coordinates of P, showing that P is the midpoint

Answer 6

Hint. The point P on the hyperbola takes the form P = (a; 3=a) for some
non-zero a.

Answer 7

sorry if thats not very clear, assign variables to the x and y coordinates of P and remember that xy=3, and it will simplify and work out

Answer 8

P(a,3/a)**

Answer 9

yeah, now find the equation of tangent line at P using that and the derivative of xy=3

Answer 10

ok ty

Answer 11

w8 then what do u do?

Answer 12

i get L(x)=3/x + -3/x^2 (x-a) for the equation of the tangent

Answer 13

well actually 3/a + -3/a^2 (x-a)

Answer 14

then what?

Answer 15

find where it intersects the y and x axes, if you put it in slope intersect form you know the y axis intercept, to find the x intercept set y=o and solve for x