# Math Assignment Help With Equations Of Tangent And Normal To An Ellipse

## 7.6.8 Equations of tangent and normal to an ellipse:

Theorem: The equation of tangent to the ellipse

x2 + y2 ‗ 1

a2 b2

at a point (x1, y1) is

xx1 + yy1 ‗ 1

a2 b2

and the equation of normal to the ellipse is x2 + y2 ‗ 1; at point (x1, y1) is

a2 b2

(y – y1) ‗ (xx1)

(y1/b2) (x1/ a2)

Proof: Let P(x1, y1) is a given point on the ellipse x<up>2 + y2 ‗  1 and Q(x2, y2) be a point on it.

a2 b2

then the equation of the chord PQ is

y – y1 ‗ y2 – y1

xx1 x2 – x1 …..(i)

as point p(x1, y1) and (x2, y2) lie on the given ellipse, therefore;

x12 + y12 ‗ 1 and x22 + y22

a2 b2 a2 b2

On subtraction we get

x22x12 + y22 – y12 ‗ 1

a2 b2

10x – 9y + 77 = 0

The equation of the normal at (-5, 3)

(77/2) [ x – (-5)] /-5 = (77/3) (y – 3)/3

### Email Based Assignment Help in Equations Of Tangent And Normal To An Ellipse

To Schedule a Equations Of Tangent And Normal To An Ellipse tutoring session
To submit Equations Of Tangent And Normal To An Ellipse assignment click here.

### Following are some of the topics in Conic Sections-Parabola, Hyperbola And Ellipse in which we provide help:

Math Assignment Help | Math Homework Help | Geometry Help | Calculus Help | Math Tutors | Algebra Tutor | Tutorial Algebra | Algebra Learn | Math Tutorial | Algebra Tutoring | Calculus Tutor | Precalculus Help | Geometry Tutor | Maths Tutor | Geometry Homework Help | Homework Tutor | Mathematics Tutor | Calculus Tutoring | Online Algebra Tutor | Geometry Tutoring | Online Algebra Tutoring | Algebra Tutors | Math Homework Helper | Calculus Homework Help | Online Tutoring | Calculus Tutors | Homework Tutoring