I'm looking for other coordinates on the curve where the tangent is parallel to y=bx+3. I have solved for a, b, c and tangent equation.
(-3,a) is on curve y=5x-7/2x+10. The tangent at (-3,a) is parallel to y=bx+3 and cuts the y-axis at (0,c).
How do I get the other coordinates on the curve where the tangent is parallel to y=bx+3?
I’m sure I need to use the gradient perpendicular to the tangent (m=-1/4) and set it equal to y=5x-7/2x+10 or y`equation and solve for x?
Any help would be appreciated.
I have solved a,b,c (-5.5,4,6.5) and the tangent equation y=4x+6.5. But graphing the curve shows me there is 2 hyperbolas so I need the points on the curve for the other tangent equation.
1. st x = -3 into y=(5x-7)/(2x+10) to get -5.5=a ;. (-3,-5.5).
2. find y` of y=(5x-7)/(2x+10). Use quotient rule..vu`-uv`/v^2.
Then you get [5(2x+10)-2(5x-7)]/[(2x+10)^2]. Then st x =-3..y`=4.
3. y`=4 is the gradient :. b=4 in y=bx+3.
4. Find equation for tangent at (-3,-5.5,m=4) using y-y1=m(x-x1). Becomes y=4x+6.5. As y=mx+c:….c=6.5.
A=-5.5, b=4, c=6.5 and tangent equation is y=4x+6.5