The equation of line parallel to the tangent to the circle x2+y2=r2 at the point (x1,y1) and passing through origin, is:

Question

The equation of line parallel to the tangent to the circle x2+y2=r2 at the point (x1,y1) and passing through origin, is: (A)  xy1+x1y=0  (B)  xx1-yy1=0  (C)  xx1+yy1=0  (D)  xy-x1y=0

Tardigrade Admin · Accepted Answer

As we know that tangent on point (x1, y1) of the circle x2+y2=r2 is x x1+y y1=r2 ldots (i) The required line is parallel to the tangent line i.e., x x1+y y1=k Since, it is passing through origin. ⇒ k=0 ∴ x x1+y y1=0

Q. The equation of line parallel to the tangent to the circle $x^{2} + y^{2} = r^{2}$ at the point $(x_{1}, y_{1})$ and passing through origin, is:

$x y_{1} + x_{1} y = 0$

$x x_{1} - y y_{1} = 0$

$x x_{1} + y y_{1} = 0$

$x y - x_{1} y = 0$

As we know that tangent on point $(x_{1}, y_{1})$ of
the circle $x^{2} + y^{2} = r^{2}$ is $x x_{1} + y y_{1} = r^{2} \dots$ (i)
The required line is parallel to the tangent line
i.e., $x x_{1} + y y_{1} = k$
Since, it is passing through origin.
$\Rightarrow k = 0$
$∴ x x_{1} + y y_{1} = 0$

Q. The equation of line parallel to the tangent to the circle x2+y2=r2 at the point (x1​,y1​) and passing through origin, is:

xy1​+x1​y=0

xx1​−yy1​=0

xx1​+yy1​=0

xy−x1​y=0