Two distinct chords through ( p , q ) on x 2 + y 2 = p x + q y , where pq  = 0 , are bisected by the x -axis. Which condition holds?

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Mathematics - Circle Question with Solution | TestHub

MathematicsCircleChord, Intercept (Made by the circle)Medium2 minQB

MathematicsMediumsingle choice

Two distinct chords through $(p, q)$ on $x^{2} + y^{2} = p x + q y$ , where $pq \neq = 0$ , are bisected by the $x$ -axis. Which condition holds?

Options:

Answer:

Solution:

If a chord midpoint is ( $t, 0$ ), its other endpoint is $(2 t - p, - q)$ . Substitution in the circle gives $2 t^{2} - 3 pt + p^{2} + q^{2} = 0$ . Two distinct midpoint solutions require discriminant $p^{2} - 8 q^{2} > 0$ .

Stream:JEESubject:MathematicsTopic:CircleSubtopic:Chord, Intercept (Made by the circle)

⏱ 2mℹ️ Source: QB

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