For a circle x 2- y 2-81- what is the equation of chord whose mid point is -2-3 A- 2 x-3 y-13-0B- 2 x -3 y -13-0C- 3 x-2 y-13-0D- 2 x-3 y-13-0

The correct option is D 2x 3y+13=0 Slope of OP is nbsp; = 32 Slope of the chord will be, m = 23 Equation of the chord will be, y = 2x3 +c Putting ( 2, 3) 3 ...

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Standard XII

Mathematics

Rectangular Hyperbola

For a circle ...

Question

For a circle $x^{2} + y^{2} = 81,$ what is the equation of chord whose mid point is $(- 2, 3)$

2 x - 3 y - 13 = 0

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2 x + 3 y + 13 = 0

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2 x - 3 y + 13 = 0

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3 x - 2 y + 13 = 0

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Solution

The correct option is C $2 x - 3 y + 13 = 0$

Slope of $O P$ is
$= \frac{- 3}{2}$
Slope of the chord will be,
$m = \frac{2}{3}$
Equation of the chord will be,
$y = \frac{2 x}{3} + c$
Putting $(- 2, 3)$
$3 = \frac{- 4}{3} + c \Rightarrow c = \frac{13}{3}$

Hence the equation will be,
$3 y = 2 x + 13$

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For a circle x2+y2=81, what is the equation of chord whose mid point is (–2,3)

The correct option is C 2x−3y+13=0 Slope of OP is =−32 Slope of the chord will be, m=23 Equation of the chord will be, y=2x3+c Putting (−2,3) 3=−43+c⇒c=133 Hence the equation will be, 3y=2x+13

For a circle $x^{2} + y^{2} = 81,$ what is the equation of chord whose mid point is $(- 2, 3)$