Question

eq of chord when mid pt is unknown​

Answer 1

Answer:

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Asked on November 22, 2019 by

Abhinab Hiran

Find the equation to that chord of the circle x

2

+y

2

=81 which is bisected at the point (−2,3), and its pole with respect to the circle.

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ANSWER

Let the chord be y=mx+c ... (i)

The line joining the midpoint of the chord to centre of the circle is

perpendicular to the circle, whose slope will be −

m

1

m

−1

=

−2−0

3−0

⇒m=

3

2

To calculate c, put value (−2,3) in the equation (i) of line

3−

3

2

×(−2)=c

⇒c=

3

13

Thus, the chord is given by 3y−2x=13

Let the pole of this chord be (h,k)

Polar of (h,k) is given by xh+yk=81

Since the chord and polar are same line, there equation must be identical

⇒

−2

h

=

3

k

=

13

81

⇒ (h,k)=(

13

−162

,

13

243

)