Equation of chord of circle {x^2} + {y^2} = {a^2} having ({x₁},{y₁}) as its mid-point is

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10-1.Circle and System of Circles

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The equation of the chord of the circle ${x^2} + {y^2} = {a^2}$ having $({x_1},{y_1})$ as its mid-point is

A

$x{y_1} + y{x_1} = {a^2}$

B

${x_1} + {y_1} = a$

C

$x{x_1} + y{y_1} = x_1^2 + y_1^2$

D

$x{x_1} + y{y_1} = {a^2}$

(IIT-1983)

Solution

(c) $T = {S_1}$ is the equation of desired chord,

hence $x{x_1} + y{y_1} – {a^2} = x_1^2 + y_1^2 – {a^2}$

$\Rightarrow x{x_1} + y{y_1} = x_1^2 + y_1^2$.

Standard 11

Mathematics

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