Question

Find the equation of tangent to the ellipse (x ^ 2)/4 + (y ^ 2)/9 = 1, which is parallel to the line x + y + 7 = 0.

Answer 1

Answer:

The slope of the required tangent is m=3.

Equation of tangent with slope m for an ellipse

a

2

x

2

+

b

2

y

2

=1 is y=mx±

a

2

m

2

+b

2

Hence, for the given ellipse the equation of tangent is y=3x±

4

45

+

3

5

(∵a

2

=

4

5

,b

2

=

3

5

)

⇒y=3x±

12

155

i.e. 6

3

x−2

3

y±

155

=0