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or is it one of the following other answers....


a. 3x + 4y - 36 = 0

b. 4x + 3y - 35 = 0

c. 4x - 3y - 23 = 0

d. 3x + 4y + 14 = 0

e. 4x + 3y + 15 = 0

f. 3x - 4y - 20 = 0

g 4x - 3y + 27 = 0

or none of these ?

2007-06-07 05:05:36 · 3 answers · asked by Olivia 4 in Science & Mathematics Mathematics

3 answers

d. 3x + 4y + 14 = 0

2007-06-07 05:13:29 · answer #1 · answered by ag_iitkgp 7 · 2 1

x^2+y^2 -2x -4y = 20

differentiating both side we have,

2x+2y.dy/dx -2-4.dy/dx =0

or, dy/dx (2y-4) = 2-2x

or, dy/dx =(2-2x) /(2y-4) = (1-x) /(y-2)

which is also slope of the tangent.

now dy/dx at x= -2 and y= -2 is = (1+2) /(-2-2) =3/-4

now equation of the tangent at the point (-2, -2) is
y - y1 = dy/dx (x-x1)

or, y+2 = (3/-4) (x+2)

or, 4y +8 = -3x -6

or, 3x +4y +14 =0
hence the correct answer is (d)

2007-06-07 05:21:35 · answer #2 · answered by sinthol 1 · 3 0

comparing given equation to the equation
x^2+y^2+2gx+2fy+c=0,we get
g= -1,f= -2
so center will be O(-g,-f)=O(1,2)
consider P(-2,-2)
m_1=slope of OP=[2-(-2)]/[1-(-2)]
=4/3
Hence the slope of tangent line at (-2,-2);m_2= -1/m_1
=>m_2= -3/4
now y=mx+c
y= -3/4x+c............(I)
since above line passes through the point (-2,-2)
-2=(-3/4)*(-2)+c
-2=3/2+c
-2-3/2=c
-7/2=c
putting this value of c in (I)
y=-3/4x-7/2
4y=-3x-14
3x+4y+14=0
so the answer is d.

2007-06-07 05:27:10 · answer #3 · answered by chapani himanshu v 2 · 2 0

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