SOLUTION: Question-1: (a): Let be the line given by the equation 3x+4y+12=0 . Find the x-intercept M and the y-intercept A of and compute the distance d between A and M. (b): Obtain

Question 251283: Question-1:
(a): Let be the line given by the equation 3x+4y+12=0 .
Find the x-intercept M and the y-intercept A of and compute the distance d between A and M.
(b): Obtain the equation of the line through M perpendicular to .
(c): Find two points B and C on whose distance from A is equal to .
(d): Find a point D that makes ABCD a square.

Question-2: Consider the circle C1 given by the equation .
(a): Find the radius r and center M of C1 and determine the points A and B of intersection of C1 with the y-axis.
(b): Find the point D of intersection of the tangent lines to the circle at A
and B.
(c): Find the equation of the circle C2 with MD as a diameter.
(d) (3 marks): Obtain the parametric equations of the circle C1 .
Question-3:
Consider the functions f(x)=(5x-4)/(3x+4) and g(x)=ln(1/6x^2+5x-4)
(a): Determine the domains of f(x) and g(x).
(b): Show that f is 1-1 on its domain and obtain its inverse.
(c): Write expressions for (fog)(x) and (gof)(x)
(d): Solve the equation f(x).exp(-g(x))=0

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Please limit yourself to one problem per submission.
You are more likely to get a response and it doesn't hog any one tutor's time.
It is ok to include a though d since they all relate to the same problem.
But that will also limit your responses.
Question-1:
(a): Let be the line given by the equation 3x+4y+12=0 .
Find the x-intercept M and the y-intercept A of and compute the distance d between A and M.
To get the x intercept set y=0 and calculate x
so after you get the intercepts plug in the ordered pairs(coordinates)
d=Sqrt((x2-x1)^2+(y2-y1)^2)
(b): Obtain the equation of the line through M perpendicular to .
convert 3x+4y+12=0 to y=mx+b format
4y=-3x-12
y=-3x/4-12
BTW -12 is the y intercept and -3/4 is the slope
A line perpendicular will have a slope 4/3
(c): Find two points B and C on whose distance from A is equal to
Equal to what??.
(d): Find a point D that makes ABCD a square.
Can't answer d without answering c

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