Analytic Geometry

The segment joining (1 -3) and (4 -6) is extended a distance equal to one sixth of its own length. find the terminal points.
How to solve this problem. I need the whole SOLUTION. THANKS

hey i need your help. please answer this question.please
1.a point moves so that the product of the distance from (0,6) and (9,0) is twice the ratio of its ordinate to its abscissa .find the equation of the locus.?

A line segment has its end on the coordinates axes and forms with then a triangle of area to 36 units. The segment passed through the point (5,2)
a). Compute the length of the line segment intercepted by the coordinates axes.
b). What is the slope of the line segment
c). compute the length segment

Guys can you help me to solve and graph this one . thanks

1. y^2=(x^2=1)(x-3)/X^3
2. x^2y-xy-x^2+10x-12y-21=0
3. y^2=x^3-9x^2+20x

Goodafternoon.,pasagot naman po ng tanong na ito,.

1. Find the equation of the circle tangent to the lines
5x + 12y - 161= 0 and 12x + 5y - 126 = 0 and passing through the point (-9,-11).

Thank you so much for your response. :-)

what is the equation of a circle touching the lines x-3y-11=0 and 3x-y-9=0 and having its center on the line 4x+y-27=0?

find the equation of the circle tangent to 3x+y+14=0 and x+3y+10=0 w/ radius square root of 10.
please someone Help me in this equations I really do need Badly some help.

can you help me with this problem; find the equations of the lines through (7, -4) passing at a distance 1 from the point (2, 1)

can anyone help me how to graph this equation

x^(3/2) + y^(3/2) = 4^(3/2)

thanks for those who will response