A line makes equal intercepts on the coordina | vedclass

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(B) Let the intercepts made by the line on the coordinate axes be $a$ and $a$. The equation of the line in intercept form is $\frac{x}{a} + \frac{y}{a

Vedclass · Accepted Answer

$2\sqrt{2}$

Vedclass · Answer

(B) Let the intercepts made by the line on the coordinate axes be $a$ and $a$. The equation of the line in intercept form is $\frac{x}{a} + \frac{y}{a} = 1$, which simplifies to $x + y - a = 0$.Since this line is tangent to the circle $x^2 + y^2 = 4$, the perpendicular distance from the center $(0,0)$ to the line must equal the radius $r = 2$.The formula for the perpendicular distance is $d = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}$.Substituting the values: $2 = \frac{|0 + 0 - a|}{\sqrt{1^2 + 1^2}}$.$2 = \frac{|-a|}{\sqrt{2}}$.$|a| = 2\sqrt{2}$.Thus, the length of each intercept is $2\sqrt{2}$.

$A$ line makes equal intercepts on the coordinate axes and is tangent to the circle $x^2 + y^2 = 4$. The length of each intercept made by the line on the coordinate axes is ...

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