Normal at a point of an ellipse:
Equation of normal is ![98_Normal at a point of an ellipse.png](https://www.expertsmind.com/../CMSImages/98_Normal at a point of an ellipse.png)
Equation of normal at (a cosθ, b sinθ) is
![1834_Normal at a point of an ellipse2.png](https://www.expertsmind.com/../CMSImages/1834_Normal at a point of an ellipse2.png)
Example: If the normals to ellipse
at points (x1, y1), (x2, y2) and (x3, y3) are concurrent, show that ![1575_Normal at a point of an ellipse3.png](https://www.expertsmind.com/../CMSImages/1575_Normal at a point of an ellipse3.png)
Solution: The equation of normal to the given ellipse at (x1, y1) is
a2xy1 - b2yx1 - (a2 - b2)x1y1 = 0 . . .(1)
Likewise the normals at (x2, y2) and (x3, y3) are
a2xy2 - b2yx2 - (a2 - b2)x2y2 = 0 ...(2)
a2xy3 - b2yx3 - (a2 - b2)x3y3 = 0 ...(3)
Eliminating a2x, b2y and (a2 - b2) from (1), (2) and (3), we find that 3 lines are concurrent if
![2291_Normal at a point of an ellipse4.png](https://www.expertsmind.com/../CMSImages/2291_Normal at a point of an ellipse4.png)
Email based Normal at a point of an ellipse Assignment Help -Normal at a point of an ellipse Homework Help
We at www.expertsmind.com offer email based Normal at a point of an ellipse assignment help - homework help and projects assistance from k-12 school level to university and college level and engineering and management studies. We provide finest service of Mathematics assignment help and Mathematic homework help. Our experts are helping students in their studies and they offer instantaneous tutoring assistance giving their best practiced knowledge and spreading their world class education services through e-Learning program.
Expertsmind's best education services
- Quality assignment-homework help assistance 24x7 hrs
- Best qualified tutor's network
- Time on delivery
- Quality assurance before delivery
- 100% originality and fresh work