Question

Find the polar of (3,--1) with respect to 2x2 + 2y = 11.
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Answer 1

Answer:

Polar of the point (x

1

,y

1

) with respect to the circle 2x

2

+2y

2

=11 is given by 2xx

1

+2yy

1

=11

Substituting the point (4,−1) into the equation will give 2x(4)+2y(−1)=11

i.e. 8x−2y=11 is the required polar.

Answer 2

The polar of ( 3, -1 ) with respect to 2x² + 2y² = 11 is 6x - 2y = 11.

Given: The point ( 3, -1 )  and the equation of the circle, 2x² + 2y² = 11.

To Find: The polar of ( 3, -1 ) with respect to 2x² + 2y² = 11.

Solution:

The polar of a point P ( x1, y1 ) with respect to a circle x² + y² = r² is given by the form,

                   xx1 + yy1 = r²                                                          ...(1)

Where r = radius of the circle.

Coming to the numerical, we are given;

The point is ≡ ( 3, -1 )

The equation of the circle is given by

       2x² + 2y² = 11

So, we can find the polar of ( 3, -1 ) with respect to the circle from (1);

         x² + y² = 11 / 2

    ⇒  3x + ( -1 )y = 11 / 2

    ⇒  3x - y = 11 / 2

    ⇒  6x - 2y = 11

Hence, the polar of ( 3, -1 ) with respect to 2x² + 2y² = 11 is 6x - 2y = 11.

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