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  4. A tangent is drawn to the circle 2x2 + 2y2 - 3x + 4y = 0 at the point A and it meets the line x + y = 3 at B(2, 1), then AB is equal to

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Q. A tangent is drawn to the circle $2x^2 + 2y^2 - 3x + 4y = 0$ at the point A and it meets the line $x + y = 3$ at $B(2, 1)$, then AB is equal to

KCETKCET 2013Conic Sections

Solution:

Equation of circle is,
$S \equiv 2 x^{2}+2 y^{2}-3 x+4 y=0 $
$\Rightarrow S \equiv x^{2}+y^{2}-\frac{3}{2} x+2 y=0$
image
Here, $A B$ is the length of tangent to the circle from $B$
i.e. $A B =\sqrt{(2)^{2}+(1)^{2}-\frac{3}{2}}(2)+2(1) $
$=\sqrt{4+1-3+2}=\sqrt{4}$
$=2$ units