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

A straight line L passes through the point of intersection of the lines $x - y + 1 = 0$ and $2x + y - 7 = 0$. If L intersects the positive x-axis at $A(a, 0)$ and the positive y-axis at $B(0, b)$, then the minimum area of the triangle $OAB$ (where $O$ is the origin) is ....

If the combined equation of angle bisectors of the lines $x^2 - 2pxy - y^2 = 0$ is $x^2 - 2qxy - y^2 = 0$, then which of the following is true?

A tangent having slope $-\dfrac{1}{2}$ to the ellipse $3x^2 + 4y^2 = 12$ intersects the X-axis and Y-axis at the points A and B respectively. if O is the origin, then the area of $\triangle AOB$ is ...