Find an equation for the line that passes through the point

Find an equation for the line that passes through the point (2, -5) and (a) has slope - 3 (b) is parallel to the x-axis (c) is parallel to the y-axis (d) is parallel to the line 2x - 4y = 3 Find an equation for the circle that has center (-1, 4) and passes through the point (3, -2). Find the center and radius of the circle with equation x^2 + y^2 - 6x + 10y + 9 = 0. Let A(-7, 4) and 15(5, -12) be points in the plane. (a) Find the slope of the line that contains A and B. (b) Find an equation of the line that passes through A and B. What are the intercepts? (c) Find the midpoint of the segment AB. (d) Find the length of the segment AB. (e) Find an equation of the perpendicular bisector of AB. (f) Find an equation of the circle for which AB is a diameter. Sketch the region in the xy-plane defined by the equation or inequalities. (a) -1 lessthanorequalto y lessthanorequalto 3 (b) |x|

Solution

Solution:

Equation of line which passed through

(2,-5)

Let the general equation of line

y=mx + c

where m is slope and c is intercept on y axis

(a) given that m = -3

y = -3 x +c

to calculate c

line passes through the point (3,-2 )

plug x = 3 and y =-2

-2 = -3*3 +c

c = 7

therefore

equation of line

y = -3x + 7

(b) if line is parallel to x axis then

then slope would be 0

ie m = 0

y =mx + c = 0x + c

y = c

Plug (-2,5)

c = 5

therefore equation of the line

y = 5

(c) line is parallel to y axis

therefore slope would be infinite

y = mx + c

that means line parallel to y axis

if it pass through

x = 3

thus equation of line is x =3

(d)

If line parallel to

2x -4y = 3

4y = 2x-3

y = (1/2)x -3/4

if two lines are parallel to each other then slope are equal

m = 1/2

therefore

y = mx+c

y=(1/2)x + c

plug (3,-2) to get intercept c

-2 = (1/2)(3) + c

c= 2-3/2

c = 1/2

thus required equation of line is

y = (1/2)x + 1/2

Answer