A circle with radius `|a|` and center on the y-axis slied along it and a variable line through (a, 0) cuts the circle at points `Pa n dQ` . The region in which the point of intersection of the tangents to the circle at points `P` and `Q` lies is represented by `y^2geq4(a x-a^2)` (b) `y^2lt=4(a x-a^2)` `ygeq4(a x-a^2)` (d) `ylt=4(a x-a^2)`

Options

A. `y^(2)ge4(ax-a^(2))`
B. `y^(2)le4(ax-a^(2))`
C. `yge4(ax-a^(2))`
D. `y=4(ax-a^(2))`

Answer

1

Explanation

Let the center be `(0,alpha)` . Then the equation of the circle is `x^(2)+(y-alpha)^(2)= |a|^(2)`.
So, the equation of chord of contact for P(h,k) is `xh+yk-alpha(y+k)+alpha^(2)-a^(2)=0`
It passes through `(a,0)`.
Therefore,
`alpha^(2)-alphak+ah-a^(20=0`
As `alpha` is real,
`k^(2)-4(ah-a^(2)) ge 0`