Question

The no. of tangents to the circle x2 + y2 = 3 which are normal to ellipse 4x2 + 9y2 = 36 is
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Answer 1

Step-by-step explanation:

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MATHS

A point on the ellipse 4x

2

+9y

2

=36, where the normal is parallel to the line 4x−2y−5=0, is?

December 27, 2019avatar

Sunita Neesa

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ANSWER

Let P(x

1

,y

1

), be the point on curve 4x

2

+9y

2

=36, where the normal is parallel to line 4x−2y=5.

∴

dx

dy

∣

p(x

1

,y

1

)

=(

9y

1

−4x

1

)

Now,

4x

1

9y

1

=2⇒9y

1

=8x

1

..(1)

Also, 4x

1

2

+9y

1

2

=36 (2)

∴ On solving (1) and (2), we get

P(x

1

=

5

9

,y

1

=

5

8

) or (x

1

=

5

−9

,y

1

=

5

−8

)