Find the equation of a normal to the ellipse x216+y29=2 at the point (4, 3).
4x - 3y = 7
In the last topic we learned how to write the equation of tangent once the points are given.
So the tangent at (4, 3) to x216+y29=2 will be x×416+y×39=2⇒x4+y3=2Slope of this line=−34⇒Slope of normal=43
We can now write the equation of normal y - 3 = 43(x−4)
⇒4x−3y=16−9=7
Using formula
The equation of normal at (x1,y1) to the ellipse x2a2+y2b2=1 is given by a2xx1−b2yy1=a2−b2⇒16×x4−9×y3=16−9⇒4x−3y=7
We can see that using formula saves a lot time. We recommend you to remember it.