SOLUTION: Find the equation of the tangent and normal to the conic 4x^2 + 9y^2 = 40 at point (1,-2).

Question 380177: Find the equation of the tangent and normal to the conic 4x^2 + 9y^2 = 40 at point (1,-2).
Found 2 solutions by richard1234, robertb:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Given the ellipse , if we differentiate with respect to x, we have

Therefore the slope at (1, -2) is
Given slope 2/9 and a point (1, -2) we can easily find the y-intercept:

Thus the equation of the line tangent to the ellipse at (1, -2) is

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The equation of the normal line: From the slope of the tangent line above at the specified point, 2/9, the slope of the normal line should be -9/2. The equation of the normal line should then be , or after simplification.
RELATED QUESTIONS
Find the equation of the normal and tangent to the curve at the given point: f(x) =... (answered by Alan3354)
find the equation of the tangents and normal to curve x^2 + 9y^2 = 25, parallel to 4x +... (answered by Alan3354)
Find the equation of a line containing the point (-2, 1) and is parrallel to the line... (answered by vidyamanohar)
Find the equation of the tangent and normal to x^2 + 3xy + y^2 = 5 at... (answered by Alan3354)
write an equation of the conic section parabola with vertex at (2,6) and directrix at... (answered by lwsshak3)
Find the equations of the tangent line and normal line to the graph of 6x^2-2xy+y^3=9 at... (answered by Edwin McCravy)
Graph the Conic Section 4x^2-9y^2=144 (answered by Fombitz)
the ellipse with equation 4x^2 +9y^2 = 36 , 2x+3y =k is tangent to the elipse, find... (answered by lynnlo)
Find the equation of the tangent and the normal : y=x�+1 at the point were x=1 (answered by ewatrrr)