Question

Find the equation of the tangent to the circle $x^2+y^2=a^{2}at(acos\alpha ,asin\alpha )$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

We saw that the equation of tangent to the circle $x^2+y^2+2gx+2fy+C=0$ at $(x_1,y_1)$ is given by $T=x{x}_1+y{y}_1+g(x+x_1)+f(y+y_1)+C=0$

$\Rightarrow Equationoftangentto{x}^2+y^2=a^{2}at(acos\alpha ,asin\alpha )$ is given by

$xacos\alpha +yasin\alpha =a^2$

or

$cos\alpha +ysin\alpha =a$

We get T by replacing $x^{2}byx{x}_1,y^{2}byy{y}_1,xby\frac{(x+x_1)}{2},yby\frac{y+y_1}{2},xyby\frac{x{y}_1+y{x}_1}{2}$ and keeping cas it is in the equation of the circle.

T=0 gives the equation of circle