Question

The equation of the tangents to the circle $x^2+y^2=13$ at the point whose abscissa is $2$, are

• A. $2x+3y=13,2x–3y=13$
• B. $3x+2y=13,2x–3y=13$
• C. $2x+3y=13,3x–2y=13$
• D. None of these above

Answer 1

The correct option is A

$2x+3y=13,2x–3y=13$

Find the equation of the tangents based on given information

Let $(x_1,y_1)$be the co-ordinates of the point of contact,
The equation of tangent to the circle will be $x{x}_1+y{y}_1=13$

Let the point be $(2,y_1)$, then
$$\begin{gathered} 2^2+y_1^2=13 \\ \Rightarrow y_1^2=9 \\ \Rightarrow y_1=\pm 3 \end{gathered}$$
By substituting the value of $x_1$ and $y_1$ in equation of tangent to the circle we get,

$2x\pm 3y=13$

Hence, option $\left(a\right)$ is correct.