Question

If a tangent drawn from the point (4, 0) to the circle $x^2+y^2=8$ touches it at a point A in the first quadrant, then the coordinates of another point B on the circle such that AB = 4 are

• A. (2,-2) or (-2,2)
• B. (1,-2) or (-2,1)
• C. (-1,1) or (1,-1)
• D. (3,-2) or (-3,2)

Answer 1

The correct option is A

(2,-2) or (-2,2)

$Equationoftangentthrough(4,0)x+y-4=0Pointofcontact=(2,2)AB=4\Rightarrow B=(2+4cos\theta ,2+4sin\theta )$
This point B lies on the circle $\Rightarrow (2+4cos\theta {)}^2+(2+4sin\theta {)}^2=8$
$\Rightarrow 16+16(cos\theta +sin\theta )$ = 0
$cos\theta +sin\theta =-1$
$\theta =\pi ,\theta =\frac{3\pi }{2}(-2,2)(2,-2)$