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  • If two distinct chords, drawn from the point (p, q) on the circle <img alt="\mathrm{x^2+y^2=p x+q y\, \, ( where \, \, p q \neq 0)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmat

If two distinct chords, drawn from the point (p, q) on the circle \mathrm{x^2+y^2=p x+q y\, \, ( where \, \, p q \neq 0)} are bisected by the x-axis, then

Option: 1

p^2=q^2


Option: 2

p^2=8 q^2


Option: 3

p^2<8 q^2


Option: 4

p^2>8 q^2


Answers (1)

Equation of the circle is

x^2+y^2-p x-q y=0
M(h, 0) be the midpoint of the chord OC 

Equation of the chord in terms of its

middle point M is S_1=S_{11}

x h-\frac{p}{2}(x+h)-\frac{q}{2}(y+0)=h^2-p h

Since this passes through (p, q)

\therefore \quad h^2-\frac{3}{2} p h+\frac{p^2+q^2}{2}=0
The roots of this equation are real

\Rightarrow 9 p^2-8\left(p^2+q^2\right)>0 \Rightarrow p^2>8 q^2

Posted by

Sumit Saini

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