A tangent having slope `-1/2` to the ellipse `3x^2+4y^2=12` intersects the X and Y axes in the points A and B respectively. If O is the origin, find the area of the triangle.

If the tangent to the circle x^2+y^2=r^2 at the point (a,b) meets the co-ordinate axes at the points A and B, and O is the origin, then the area of the triangle OAB is

Draw the graph of x+y=6 hich intersects the X-axis and Y-axis at A and B respectively. Find the length of seg AB and the area of /_\ AOB, where point O is the origin.

For the ellipse 3x ^(2) + 4y ^(2) =12, the length of latus rectum is

Draw the graph of x+y=6 which intersects the X-axis and Y-axis at A and B respectively. On the same graph paper, draw the graph of 2x-y=3 which intersects the X-axis and Y-axis at C and D respectively. E is the point of intersection of both the graphs. Find the areas of /_\ ECA /_\ EBD.

If tangents are drawn to the circle x^2 +y^2=12 at the points where it intersects the circle x^2+y^2-5x+3y-2=0 , then the coordinates of the point of intersection of those tangents are

The circle x^2 +y^2=4x+8y+ 5 intersects the line 3x-4y= m at two distinct points, if

Show that the line 8y+x=17 touches the ellipse x^2+4y^2=17 . Find the point of contact.

Find the equation of the tangent to the ellipse x^2+4y^2=100 at (8,3).