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find the equation of the tangent to the parabola y^2-6x+8y-6=0 which is inclined at an angle of 45 degree to the x axis. Please answer as soon as possible.

find the equation of the tangent to the parabola y^2-6x+8y-6=0 which is inclined at an angle of 45 degree to the x axis. Please answer as soon as possible.
 

Grade:11

3 Answers

Susmita
425 Points
3 years ago
y2-6x+8y-6=0
derivate wrt x.
2ydy/dx-6+8dy/dx=0
Or,(2y+8)dy/dx=6
Or,dy/dx=6/(2y+8)
Also dy/dx=tan45=1 given
So 2y+8=1
Or,y=-7/2=-3.5
putting this value of y in equation of curve
x=5.7 (you can also express it in p/q form.i am writing in decimal form as it helps typing).
so equation of tangent is
y=mx+c=x+c and it passes through 5.7,-3.5.
So c=-9.2
y=x-9.2
 
Susmita
425 Points
3 years ago
Oops!that would be
2y+8=6.
Or,y=1
So x=0.5
Please correct it.and follow the steps.thank you.
.........................................................................
 
Deepak Kumar Shringi
askIITians Faculty 4405 Points
3 years ago
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