The angle between the tangents to the circle | vedclass

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Question

(D) The equation of the circle is $x^2 + y^2 = 169$,which has center $(0, 0)$ and radius $r = 13$.The equation of the tangent to the circle $x^2 + y^2

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(D) The equation of the circle is $x^2 + y^2 = 169$,which has center $(0, 0)$ and radius $r = 13$.The equation of the tangent to the circle $x^2 + y^2 = r^2$ at point $(x_1, y_1)$ is given by $xx_1 + yy_1 = r^2$.For the point $(5, 12)$,the tangent equation is $5x + 12y = 169$. The slope $m_1 = -\frac{5}{12}$.For the point $(12, -5)$,the tangent equation is $12x - 5y = 169$. The slope $m_2 = \frac{12}{5}$.Since $m_1 	imes m_2 = (-\frac{5}{12}) 	imes (\frac{12}{5}) = -1$,the tangents are perpendicular to each other.Therefore,the angle between the tangents is $90^o$.

The angle between the tangents to the circle $x^2 + y^2 = 169$ at the points $(5, 12)$ and $(12, -5)$ is ............. $^o$.

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