Locus! (1 Viewer)

[sf_diegoxrock]

what is the eqn of the locus if it crosses the lines
4x-3y+2=0 and 3x+4y-7=0
thanks so much

 

[Riviet]

I think it's just the intersection point of the two lines
y=(4x+2)/3 (1)
y=(-3x+7)/4 (2)
solve 1 and 2 simultaneously:
16x+8=-9x+21
25x=13
x=13/25
.: y= 102/75
I'm probably very wrong lol.

 

[SoulSearcher]

u got it right

just simplifying the fraction here,

y = 34/25

therefore the point of intersection is ( 13 / 25 , 34 / 25 )

 

[sf_diegoxrock]

urgent: tangents + directrix

find the equation of the normal to the curve x^2=-2y at the point (4,-8). This tangent meets the directric at point M, what are the co-ords of point M?

thanks so much..!

 

[pLuvia]

x²=-2y
y=-x²/2
y'=-x

At (4,-8)
y'=-4

Eqn of tangent

y+8=-4(x-4)
y=-4x+8

-----------------------------------------------------

x²=-2y
|4a| = -2
|a| = -1/2
a = 1/2

Vertex = (0,0)

.: Directrix y= -1/2

Tangent y=-4x+8

Intersection

-1/2 = -4x+8
x = 17/8
y = -1/2

M( 17/8 , -1/2)

 

[tacuric]

Damm, I've not done locus since last term. i'd like to help, but i have to go and read some notes. Otherwise i'd help.